There might be shortcuts for some points, and some info might be already available, but the general route is:
1. Figure out how the mobile app controls the drone
2. Re-produce that by writing an app which controlls
Tello from a PC, or Raspberry Pi, or any other computer which is easily accessible and known to you, and based on Linux
3. Find a way to log into the Linux working on Atheros chip within the RC, get root access
4. Figure out how a service working on the Atheros chip receive information about all the sticks and buttons, which is later sent through Wifi to Mini (by either reverse engineering or experimentation)
5. Update your Linux code so that it can get the stick values in the same way Atheros chip does
6. Cross-compile your application using toolchain from Atheros SDK (it may be just the normal ARM toolchain, I don't know)
7. Replace the service running on Atheros chip with the one you created