Batteries always go in carry on luggage.
juice can be in carry on or checked luggage (not my favorite as if it spills, well, that's what your were planing to wear when you arrive). Me? Everything in my carry on. Batteries in sleeves or boxes,
juice in a 1 quart Baggie just like any other liquid you fly with. I never travel long enough that 2 or 3 30 ml bottles won't hold me through a trip, but I only vape about 5 ml a day. Truthfully even less when traveling as I usually go with mtl higher resistance setups with a higher nic
juice so I can stealth vape easily.