I have the DJI Fly app on my iPhone, signed into the same account that is on the Fly app on my RC.

How do I sync the content so the app on the RC and on my iPhone are the same?

Hi there. Thanks for reaching out. If you're referring to the Flight Records, you may sync it by following these steps:
1. Go to the DJI Fly app>Profile>More>Flight Data Center.
When "Auto-sync Flight Records" is not enabled, there will be a pop-up window that asks whether to enable it once you enter this page:

If the pop-up prompt is canceled, you can still select the quick button "Enable" that displays at the top of this page:

2. You can manually enable it by going to Profile >Settings>Sync Flight Data>Auto-sync Flight Records.

If this is not the content you're referring to, kindly specify it so we may check it for you.
Should you have further concerns, please reach back here at DJI Forum. Thank you, and have a nice day.