There's a lot of controversy over that. If you're talking about flare buddies, no, it's a bad idea. That causes stress, which weakens your fish over time and quickly makes him susceptible to all kinds of problems.
That said, a very brief (like, less than a minute) flaring session with a mirror a couple of times a week can be seen as very healthy and a good idea. One, it gets blood flowing to the fins, which can increase color, improve their resilience to damage and disease, and it also gives your betta a tiny shot of adrenaline, momentarily boosting all over healthy. In tiny amounts, this isn't a bad thing. It when it happens for a long time or in quick intervals, it quickly leads to stress build up.
For you, the owner, the mirror idea can be a good thing. This allows you to fully check up on your bettas' health. Are his fins in good condition? What about his gills? Does he react quickly? Does he react at all? How does he act after the mirror has been put away? Does he show stress lines? (These are horizontal bars along his body. )
The bored part is purely subjective. I rarely do mirror flares with my boys because Quinn carries his fins in flare posture all the time (not full flare, but they are always held proudly) Boba doesn't hold still long enough to see his reflection in a mirror. Möbius flares a bit, but not for very long before he just drifts off somewhere else.