I said I'd report back after testing the current beta of FlickType in full screen mode on my iPhone SE 2020 running iOS 14.2. First, let me say that I leave my keyboard set to English US with touch typing as the default mode. I find this setting is easiest for inputting short text such as user names and passwords or for quick searches. Second, I primarily use the FlickType keyboard when I'm typing either text messages or emails on my iPhone. If I need to input something longer than these, I'll use my computer's full sized keyboard and transfer the input to my iPhone using the KeyWi keyboard. Finally, ever since upgrading to iOS 14, the FlickType keyboard does not respond when launched in full screen mode when you start tapping keys to enter text. In my case, if I immediately start tapping keys on its launch, no tap sound feedback is provided and I'll get a funny audio sound sort of like the iPhone is burping.
After extensive testing with the Messages app, the following steps work best for me to get FlickType typing correctly in full screen mode:
1. Place focus in the text box and double tap to make sure the on screen keyboard has launched.
2. Find by touch the Next keyboard button in the lower left of your screen and double tap and hold and slide your finger up until FlickType is announced and then release.
3. You will be in FlickType full screen mode. To activate Direct touch so that FlickType works correctly, do the rotor turn gesture once either clockwise or counterclockwise and immediately do it once again in the opposite direction. Direct touch should be announced and single finger swipe down once to turn it on.
4. FlickType should now work as it has in prior versions of iOS.
5. To exit out of full screen mode, single finger slide up the screen and you'll be returned to the US English on screen keyboard for sending your message.
Someone posted here that turning Voiceover off and back on would turn on Direct touch so that FlickType would work correctly but this was not my experience. Remember that your results may vary based on your device and its settings.
I realize that the above requires a few steps that hopefully will be reduced in future iOS versions. In any event, these steps provide the minimum number of taps and gestures needed to get FlickType working in full screen mode under iOS 14.x.
Take care and stay safe.