If you're wondering "dang, why does the tapejara fly not as fast as expected, i can't even catch up to a wild tapejara. do i need less weight? lemme get rid of some items." then you're right. The tapejara loses about 55% of its movement speed when its tamed, but the game "compensates" the loss by buffing its movement speed to like 250% so that it is almost as fast as a wild tapejara, but it is exacerbated by the fact that you will usually be riding the tapejara while its weight is about 40% occupied.