There should be a solenoid that activates when the engine is running to charge the house battery OR on some Fords there is an OE circuit for charging the aux battery. I had that on my 94 E350 Chinook and it went bad. Instead of fixing it I put in a combiner relay so if either battery was charging they would combine and both charge.
If the gennie is truly flooding the carb may well be gunked and need a tear down. If there was an ignition failure in the gennie you'd smell fuel as it would not be getting burned.
If you determine it truly is flooding make sure you check the oil. A bad flooding situation can end up with a bunch of gas in the oil which is not good. I just dealt with that on a Honda generator.
