Long thread, but hopefully the thing that worked for my DJI Go app with my drone will help here.  My issue was with all the memory that the app was taking up.  The original thread here seems to point in that same direction.  If so, here is the SIMPLE SIMPLE fix that removed 2 gigs of data from my iPhone:
Open DJI GO app
Tap "Me" in the bottom right corner
Tap the gear in the top right corner
Tap "Clear Cache"
A list of various caches will be displayed with an option to clear some or all.
Lemme know if I win the long thread contest here  

StanfordWebbie Posted at 2017-10-21 19:53
Long thread, but hopefully the thing that worked for my DJI Go app with my drone will help here.  My issue was with all the memory that the app was taking up.  The original thread here seems to point in that same direction.  If so, here is the SIMPLE SIMPLE fix that removed 2 gigs of data from my iPhone:
Open DJI GO app
Tap "Me" in the bottom right corner

Cleared up a big 95 megs of the 9+ gigabytes loading up my iPhone.

Wow! Finally got the answer from DJI Thailand support! For all of us lucky iPhone Users, there is a special trick that Android users don't get to use ...

Your iPhone needs to be connected to your Osmo Mobile. Once on, hit the little playback triangle. Once there, select what you need to delete, a trash can will appear at the upper left. hit that and your iPhone storage will thank you!

StanfordWebbie Posted at 2017-10-21 19:53
Long thread, but hopefully the thing that worked for my DJI Go app with my drone will help here.  My issue was with all the memory that the app was taking up.  The original thread here seems to point in that same direction.  If so, here is the SIMPLE SIMPLE fix that removed 2 gigs of data from my iPhone:
Open DJI GO app
Tap "Me" in the bottom right corner

OUCH!  I had hoped for better results - it did with my Mavic/iPhone combination.  I ordered my Osmo with the Black Friday price discount - arriving on Wednesday.  I'm saving your subsequent posting about how you DID get an Osmo solution.  I expect I'll run into your problem and will use your fix.  Thanks, good filming to ya.  

StanfordWebbie Posted at 2017-11-27 07:15
OUCH!  I had hoped for better results - it did with my Mavic/iPhone combination.  I ordered my Osmo with the Black Friday price discount - arriving on Wednesday.  I'm saving your subsequent posting about how you DID get an Osmo solution.  I expect I'll run into your problem and will use your fix.  Thanks, good filming to ya.

If you are using an iPhone, the method you quoted didn't work for me; it only cleared less than 100 megabytes. I had to use the method given to me by DJI Thailand. That cleared all the videos and photos stored within the app.

Curt1591 Posted at 2017-11-27 13:27
If you are using an iPhone, the method you quoted didn't work for me; it only cleared less than 100 megabytes. I had to use the method given to me by DJI Thailand. That cleared all the videos and photos stored within the app.

My problem (DJI GO and iPhone 7) : I can't delete the files in the hg300 storage folder.  After trying all the suggestion above (and waisting time) I delete / reinstall the DJI GO app on my iPhone.  Much faster and easer. After setting up my preference, I'm back in business

This response deals with recovering your iPhone memory, as opposed to securely deleting photos and videos on the iPhone.
The iPhone memory can be recovered by using iTunes to bulk delete all the DJI OSMO videos and photos. This is achieved by deleting the 'HG300 Storage" file from the DJI GO app on the iPhone. After connecting the iPhone to iTunes, select 'File Sharing' and then select the 'DJI GO' app. From the documents list select  the 'HG300 Storage" file and delete using the keyboard. Memory recovery can be confirmed on the iPhone using Settings/General/iPhone Storage. The 'VideoCache' file may also need to be deleted, however I haven't done that, as my file was quite small due to manually deleting most of the videos using the editor on the DJI GO app on the iPhone.

This worked on Windows, and I imagine should work on a Mac.

This response deals with recovering your iPhone memory, as opposed to securely deleting photos and videos on the iPhone.

The iPhone memory can be recovered by using iTunes to bulk delete all the DJI OSMO videos and photos. This is achieved by deleting the 'HG300 Storage' folder from the DJI GO app on the iPhone. After connecting the iPhone to iTunes, select 'File Sharing' and then select the 'DJI GO' app. From the documents list select  the 'HG300 Storage' folder and delete using the keyboard. Memory recovery can be confirmed on the iPhone using Settings/General/iPhone Storage. The 'VideoCache' folder may also need to be deleted, however I haven't done that, as my file was quite small due to manually deleting most of the videos using the editor on the DJI GO app on the iPhone. The folder/s will be automatically replaced after recording another video on the iPhone using the DJI GO app.

A similar process can also be used to bulk copy the DGI GO videos and photos to a computer. After highlighting the 'HG300 Storage' folder (obviously before deleting as described above), use the scroll bar to scroll to the bottom of the document list and select 'Save to...'.

This worked on Windows, and I imagine should work on a Mac.

This response deals with recovering your iPhone memory, as opposed to securely deleting photos and videos on the iPhone.
The iPhone memory can be recovered by using iTunes to bulk delete all the DJI OSMO videos and photos. This is achieved by deleting the 'HG300 Storage' folder from the DJI GO app on the iPhone. After connecting the iPhone to iTunes, select 'File Sharing' and then select the 'DJI GO' app. From the documents list select  the 'HG300 Storage' folder and delete using the keyboard. Memory recovery can be confirmed on the iPhone using Settings/General/iPhone Storage. The 'VideoCache' folder may also need to be deleted, however I haven't done that, as my file was quite small due to manually deleting most of the videos using the editor on the DJI GO app on the iPhone. The folder/s will be automatically replaced after recording another video on the iPhone using the DJI GO app.

A similar process can also be used to bulk copy the DGI GO videos and photos to a computer. After highlighting the 'HG300 Storage' folder (obviously before deleting as described above), use the scroll bar to scroll to the bottom of the document list and select 'Save to...'.

This worked on Windows, and I imagine should work on a Mac.

I found it easy to clear all the DJI clutter by simply deleting the app and reinstalling it.

I’m a Mac guy - Think Different

In order to completed files on the iPhone, you'd better to use Mobikin iOS Data Eraser to meet your demands.
The program can provide users with 3 different security levels for erasing. The wiped data by the program will never be retrieve by any data recovery software on the market.

Ok - I just spent an entire night and morning wishing I had never even heard of DJI Osmo 2. We had a rehearsal yesterday and now I need footage from my phone cleared for the ACTUAL event today.

I am in a remote shooting location without internet and my phone IS NOT DELETING ANY VIDEOS

YES i've cleared the cache

YES i've verified that iphoto "deleted immediately" and that videos aren't in the photo cloud or on the phone

YES i've deleted the videos from the player WHILE the OSMO was connected.

NO I cannot delete and reinstall the app

NO these videos aren't playing back or transferring correctly without glitching, premiere, VLC and quicktime all glitch out on iExplorer export, apple file export, an ditunes/photos just plain refuses to import the footage, but decides to sadistically wait until the 1 hour footage batch transfer process is about to complete before "kindly" informing me that the file transfer failed.

YES airdrop works, but since we're shooting in 4k, it takes FOREVER and I only discovered that workaround this morning. (30 min transfer for one 7 min clip that I have to make sure I don't miss the airdrop "accept" button window and have to restart for EVERY FILE.)

THIS IS HORRIFYINGLY UNNACEPTABLE - DJI DO YOU EVEN USE THE APPS YOU RELEASE??? USING YOUR APP IS MAKING MY PHYSICALLY ILL AND OUR SHOOT IS RUINED BECAUSE OF THESE BABYTOWN BUGS THAT YOU NEVER SAW FIT TO WORK OUT.

MAKE.YOUR.VIDEO.FILES.DRAG.AND.DROP - or AT LEAST PROVIDE DOCUMENTATION ON HOW TO DO IT!!!!!!!

WHY IS THIS SO HARD? THIS IS A JOKE!