Will I still be able to use the Eon-Flute and soar in the sky or is that feature impossible for me to use after giving away the mega stone?
Releasing or trading the Eon Pokemon doesn't stop it from coming when using the Eon Flute. Weirdly, the Mega Evolving animation will still happen if you toss or give away the Mega Stone. Giving away the Mega Stone will still allows you to soar on Latias/Latios.