Because the 'once per turn' part of Boast comes from the rules of the ability and isn't written out at the end of the ability, I would assume this is correct behavior, and even if a creature has multiple Boast abilities it can only Boast once per turn.
- 702.142. Boast
- 702.142a A boast ability is a special kind of activated ability. “Boast — [Cost]: [Effect]” means “[Cost]: [Effect]. Activate only if this creature attacked this turn and only once each turn.”
- 702.142b Effects may refer to boast abilities. If an effect refers to a creature boasting, it means its boast ability being activated.
I think the wording of Birgi also supports this reading of the ability.
Birgi, God of Storytelling {2}{R}
Legendary Creature — God
Whenever you cast a spell, add {R}. Until end of turn, you don’t lose this mana as steps and phases end.
Creatures you control can boast twice during each of your turns rather than once.