I recommend using the full charge voltage, and accounting for charger efficiency. But you are also accounting for the cells twice in your comments, that’s not needed. EDIT, you got it!

(350W x 80% efficiency) / (3 cells * 4.2V/cell) = ~22.2 amps total. ~11.1A for each battery.

Isn’t that a 20 amp charger? Which is good, as that would leave your 350W power supply a little extra breathing room. 20 amps on the charger, 10A to each pack. Just about perfect, assuming the supply rating is honest.