Sorry this is a long one..
I've had my Mavic  2 weeks now and only taken it out twice and both times were a disaster.

It's a really strange one. After trying two differnt phones with no luck I thought I'd found one that was fine, but no..  So the first phone (Cubot Rainbow 2) the screen just turns to mush as soon as there is any movement, the second phone (Leegoo Alfa 5) works ok but the DJI App just crashes every 2 minutes. So I tried a friends Nexus 4 and it was clear and faster updating than both so I thought great and bought a used one off Ebay. Yesterday was my first outing with the Nexus and all was fine until about 3 minutes in to the flight the phone just switched off (I assumed I'd hit the power button by mistake as I was not looking at the phone and was flying LOS) .

So I powered it back up without unplugging and noticed it was on 2% and saying charging, flew for 2 more mins and shutdown again. I then unplugged the phone from the remote and switched it back on and it came back up with 90% battery.. Plugged it back in and now showing 90% and charging, another minute of flying and boom 0% and shutdown. Unplugged from remote turned it back on and 90% again, decided to give up and consigned myself to having to send back a faulty phone.

Got home, phone was still on standby and registering 89% so I ran geekbench and left youtube running video playlists for 3/4 of an hour and got it down to 45% before I decided it was definitely not the phone battery at fault.

Here's what I've tried ..
Unistalled DJI Go / re-installed
Turned off video cacheing (was a tip in Iphone Battery Drain thread).
Rest phone to factory with DJI Go the only App
Running in Airplane mode.

Last night I wipped it again and installed just Lichi (Purchased for my P3P a while ago).
This morning exactly same thing.. after a few mins of flight phone shut down reporting 0% battery, unplug and turn back on it was actually at 80%.

Has anyone experienced this?
Things I've yet to try..
running the phone off the secondary USB port on the remote and not off the mini USB C
Buy a Ipad Mini 2 ?

Just run the same Nexus 4 on my Phantom 3 pro for 20 mins without a problem (phone dropped 5% 50%-45%).

Ideally I'd like a phone that clamps straight in to keep the Mavics compactness relevant and would rather not lug around tablet adaptors and my Hudl 2 (which is great on the Phantom.)

I'm thinking something in the way the Mavic remote charges the device is changing the voltage level incorrectly and tricking the phone into thinking it's empty or an overcharge cut out.

The using a USB cable to the bottom of the remote instead of to the side.  See if that makes a difference.

From what you are telling me, it sounds like your phone is trying to charge or power the remote.