If your flat bed trailer just has the electric/surge brakes on it and nothing else then the trailer battery will only be used for the electric or surge trailer brakes. Most of the larger utility type flat bed trailers have the surge type brakes that don't need the brake controller on the truck side.
The safety lights etc for these type trailers are all powered by the truck battery system..
The batteries I have seen are small sealed throw away types and sealed up in a compartment box on the tongue area. They are not a very large battery... The only time they would be used is in the event the trailer becomes disconnected. The trailer breakaway switch action turns them ON...
I guess your setup must be different than what I am familiar with...
NOTE I was just on the etrailer.com site and they have a video for installing a hopkins battery charge kit...
ETRAILER HOPKINS Battery Charge Kit
Roy Ken