Agreed with everyone here. Bring your camera bodies, lenses, and chargers with you. Everything else, put it in check-in. That includes the speedlite, battery grips, cleaners, etc. Basically, you'll want to bring with you the bare essentials you'll need to perform a shoot even if your checked in luggage gets delayed. So camera, lens, batteries, charger (only one if you have multiple of the same kind as that's all you really need in a pinch), and memory cards. Everything else, you can probably pick up at a store in an emergency, or isn't absolutely necessary to take a simple picture. Put the tripod/monopods in the checked luggage as well as some airlines may give you grief (it's very inconsistent).
Only if you have extra weight capacity afterwards should you add more stuff to your carry on, probably in order of most expensive first (ex. speedlite).
Double check the airline's policy on lithium batteries; some say that they don't want them in checked luggage unless they're installed in a device (guess they're concerned with explosions being unchecked), and some airlines even have restrictions on the amount of lithium you can bring on board, although for the most part, if they're protected from external short circuiting by using proper battery covers or holders, it should be fine (although realistically, that doesn't have much to do with a li-ion battery's tendency to explode as that more comes down to the way the battery was constructed in the first place and whether or not there's too many bits of metal or other contaminants floating around that can puncture the inner separator of the battery causing a short-circuit within the battery that can trigger an explosion, but hey, security officials have to look like they're doing something about it, right?).
