I have never heard that constant flaring leads to tail biting. I never card my bettas (and won't till I show them) and I've never had a tail biter.
Who am I? Well I am a Junior Member of the International Betta Congress and a breeder of white HMPKs, red dragon HMPKs, black/red dragon HMPKs, metallic multi HMPKs, blue masked HMPKs, and now multi color HMs. Soon to add black HMs. I will be showing in New Breeder class in fall of 2012.