Captain Flynt is the leader of the Bandits at the Soaring Dragon camp. He was the previous owner of Claptrap until Claptrap tried to mutiny and steal the Captain's ship. After that, Claptrap fled and began giving the Captain tribute in the form of loot in exchange for being left alone.
Captain Flynt is a rather tough guy so it's going to take a good amount of ammo to take him down. He'll start off the battle at the top of the ship. While he's up there, alternate between taking pot shots at him and keeping the Marauders on the lower level at bay. If you stick to the far left or right side, you'll be decently protected by Flynt's height advantage. After you deal some damage, watch out for his Grenades. He'll then jump down onto the ship to get closer.
At this point, you're going to encounter your first elemental enemies. There are some Psychos that will be on fire and deal fire damage to you. Flynt will also be carrying fire based weapons. If you get hit, you'll catch fire and receive damage slowly over time. They are all relateively close range so it's important that you keep a good distance on them. Also be very careful of the things that look like trap doors on the floor connected by large pipes because these can open up and spew fire at you.
Keep moving and perhaps switch to a rapid fire weapon with good mid-range accuracy. This will probably be your best bet by keeping you at a distance while dealing maximum damage. At this point, you'll likely also have access to yourAction Skill so don't forget to use that as it'll likely make this fight significantly easier.