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As near as I can tell, the TSA regs allow you to travel with a total of four "medium size" (100WH to 300WH capacity) batteries:
1. one battery, installed in a device, in checked luggage
2. one battery, installed in a device, in carry-on baggage
3. two spare batteries, not installed in a device, in carry-on baggage
I don't think that the TSA permits you to travel as a passenger with more than that. You can ship more, as air cargo, but there are a bunch of requirements for special packaging and paperwork that probably make that impractical for a routine shoot.