Depending on how many btu's the burner is, the battery will not last unless you have the truck engine running without a lot of accessories on while the alternator is making electricity.
Some burners need 20 amps, some need 40 amps for the larger burners.
I would not use a battery charger as it is not engineered for that use and that could potentially be a fire hazard when it overheats.
Maybe having a larger alternator installed with a very large marine battery and have someone wire the battery to the truck charging system.....maybe.
I would call Russ J about it and get his opinion.
You would be better off changing out the engine for one that has a charging circuit for the proper amps needed for the burner to run.