I use the AO Cooler 18 pack for my SeaFrogs Salted Line a6xxx, 1 strobe, arms, grip and tray. It barely fits if you fold in the arms. The cooler folds flat and goes in my check-in bag; it is very bulky, even when folded. The housing, camera, etc. go into my carry-on backpack.
For a full frame, 2 strobes, arms, etc., a 24 pack would be a very tight fit, if it fit at all. The larger cooler would be a safer choice but you will have to measure to see if it would be an allowable, carry-on size. I would also recommend that you fold up your rig as compact as possible and measure the dimensions for comparison to the internal size of the coolers. The height is problematic for me with the 18 pack.