I install Android Studio via flatpak, and this can cause flutter doctor to not be able to determine the version or to not recognize the installation at all. I've managed a hacky fix for this by running a few commands that I run as a simple script that I'm sharing here. If you use this, just close Android Stuido after it is opened; it seems to just need to be opened once in order to be recognized by flutter doctor.
#!/bin/bash
flutter config --android-studio-dir=/var/lib/flatpak/app/com.google.AndroidStudio/current/active/files/extra/android-studio
/var/lib/flatpak/app/com.google.AndroidStudio/current/active/files/extra/android-studio/bin/studio
flutter config --android-studio-dir=""
flutter doctor