Yes, you can fly with this gear! We have customers who take their Canadian Board Co. setup from YVR to Cabo every winter.
The BLU3 System:
The lithium-ion batteries are removable and fully TSA-compliant.
Rule of Thumb:
Always pack the batteries in your carry-on luggage (do not check them). The main compressor unit and hose can be safely checked with your regular luggage or brought on board.
The Paddle Board:
Your iSUP rolls up into its wheeled travel bag, which can be checked as standard sporting equipment (often flying free depending on your airline!).