BA would be going backwards if they bought flybe. Remember much of today’s flybe is the remains of the loss making BA CONNECT operation which was the succesor BA CitiExpress which followed the mess that was British Regional Airlines and the merger with Brymon which fused loss making BA mainline regional with their former franchise partners. None of this made money, ever in the case of mainline or since the 90s in the case of BRT and BRY.
The raison d’etre for BA Cityflyer is to connect high yield LONDON City to Europe, BA cannot make money outside of the London market, never could. Hence there is no sane reason for IAG to buy back their former loss making regional routes which remain loss making and don’t feed mainline.