I wouldn't tap the glass trying to get him to flare. Glass tapping is very stressful to fish. If you hold up a mirror and he doesn't flare it just means that you have a smart betta.
My first betta (betta 1) never flared, no matter what was going on around him. I held up a mirror to see what would happen and he glanced over and continued on his way. I added a second betta (separate tanks, side by side) and had to set up a divider so they couldn't see each other. Betta 1 goes nuts over betta 2, flaring and swimming straight into the glass to attack betta 2.
I'd just say you have a smart boy that isn't fooled by the mirror.