I can make a try. The unit of Ampere is Coulomb per second. In the datasheet of the FET you can find how many Coulomb it takes to charge the gate. Lets use Total Gate Charge (Max.) Qg = 227 nC. Since you are using f = 40kHz, total charge moved to the gate in one second is Q = Qg * f = 227nC * 40kHz = 9mC. This means that the average current is I = Q / t = 9mC / 1s = 9mA per FET + losses. Since you have 6 FETs, the total average current is 9mA*6 = 54mA + losses. So that's what drains the 3s battery.
The heat in your wires comes from the RMS current. In this case, the RMS current is a lot higher than the average, since the current is pulsed into the gates with high peaks. Lets say the gate current is a 1A rectangular pulse. This means it has a duty cycle of 0,009. Irms = 1A * SQRT(0,009) = ~0,1A to charge the gate. Since the current that discharges the gate passes through the same wire, then Irms_tot = 0,2A. If the ground wire is shared, it has to pass the RMS current from the 3 lower FETs gates + the RMS current which charges the bootstrap caps. This means the RMS current in a shared ground wire is probably in the order of 1A RMS.
If there is shoot through in the buffers, or some other unwanted losses, then both average and RMS gets higher, of course.