I have had 0 problems with my air 2 with 4 batteries. TSA has said nothing. These have been domestic flights only so far. IF going to another country you MUST get their current drone regs for foreign operators entering their country.
Also place some painters tape or duct tape over the exposed battery terminals of the batteries NOT mounted in the aircraft. This protects from short circuiting the battery - a known fire hazard. All the batteries must me in your carry on bag.
There's no problem carrying the drone on a plane, people do it every day.
The drone can go in your checked luggage or carry-on, but the batteries must be in carry-on.