Baby B'air is not FAA approved, most if not all carriers do not allow its use for taxi, takeoff and landing, and some don't allow its use at all.
Since I fly AA and Delta often I know they prohibit its use,
here is a link to AA's regulations
https://www.aa.com/content/travelIn... Restrictions
In case my link dosen't work here is a quote:
These are the Non-Approved:
"FAA Non-Approved Infant Seat or Child Restraint Devices
The following may not be used when an infant seat or child restraint device is required:
Any device without an approval label
Booster seats without an approval label or shoulder harness
Belt extensions that attach to the parent or the parent's restraint
Any device that positions a child on the lap or chest of an adult "
Southwest, Delta and Jet Blue have similar wording.
Best advice is to check your specific carrier to see if and when BBA is allowed. They may even have a section on the webstie on flying with children.
I have seen FA's not allow the BBA and most parents have complied, those that didn't had the BBA confiscated for the duration of the flight.
HTH
TJ