No.

The only remotely possible thing is if you have "too many" cards with Chase at present, even if they're of different kinds. I'm not familiar with specifically how this may work with Chase, but I know people used to run into it with Citi back when Citi allowed you to apply for 2 AA credit cards (and get the bonuses) every 60ish days. If you didn't cancel them and let them build up, after a few rounds of this you would hit the limit (maybe 6 or 7 or so Citi cards total, and may have varied from person to person).

Since Chase doesn't let you reapply for the same cards with the same frequency, there's way fewer people getting into that situation with Chase.

But again, this ("too many" cards with us) is a credit decision, not a bonus decision.

Bonuses tend to be given out independently for completely different programs.

I had to add "completely" because we've heard some tales that Chase may be rejecting people for the CO bonus if they have a UA card (or vice versa), because "we know they're in the process of merging". But that doesn't apply to BA (even if BA is merging with someone, and I think their relationship with IB may be considered a merger, Chase doesn't have a card already with whoever they might be merging with).