Just solved it for you.
Writeup following in a few minutes.
Edit: Sorry - same hangup. :/ Had the menu key working in tasker, but not in third party apps.
input keyevent 82
gets executed by tasker in tasker, but not while a third party app is running. Google sources reconfirm, that you need root for that.. :/
edit: Tapping multiple times onto the version number under device info will enable developer options in settings, in developer options you can enable usb debugging. Then you can adb into the device. Then you can run:
adb shell 'am start -n com.bfv/com.bfv.BlueFlyVario --user 0 && sleep 2 && input keyevent 82'
Which will bring up the menu in the app you requested. Sad thing is, if you run the command locally - it will not. At this point _everything_ points towards you needing root for this action.

(Or an app that somehow manages this using accessibility settings permissions)