I dont think you need a mirror - I have heard that a mirror backing to the tank can cause problems with stress levels in the Betta which is why I covered the backing of my tank with a backround!!
He just seems to Flare cos he wants to ! Maybe he can see his reflection in the tank glass side when the lights are on ?? I dont know ??
He does only seem to do it when I feed him (Bloodworm)
How long have you had your Betta Spanair ?? Maybe he is just really chilled out and does not want to flare ??
Let me know how it goes
Jay