The vehicles available to your raid are:
Demolisher x 2(n) x 5(h)
Siege Engine x 2(n) x 5(h)
Chopper x 2(n) x 5(h)
Normally groups leaving up no towers will use the pure burn method, that doesn't involve launching any players on top of Flame Leviathan to take out turrets and never triggers a shutdown. With this method every vehicle is used. However, leaving up four towers requires a different approach.
In order to defeat Flame Leviathan with four towers up the raid must launch players to trigger shut downs. However, if you're using two or five of each vehicle this means that the Demolisher drivers will run out of Pyrite, lose their stacking DoT, and therefore the vast majority of the raid's damage. To counter this, you have to switch up the vehicles.
For a 10-man group attempting 4-tower FL, the following vehicle breakdown is recommended:
Demolisher x 2
Siege Engine x 2
Chopper x 1
As you can see, this leaves a "free" player with no vehicle. What we do instead is have three people assigned to one Demolisher. One driver and two alternating gunners/launchees. When the fight is about to begin, the first launchee loads into the launcher and the second loads into the gunner seat. As soon as FL is engaged the first player gets launched and takes out both turrets on his own. Elemental Shamans, Warlocks, and Moonkin Druids are particularly well suited because they can heal themselves a little bit before being parachuted off of FL's back.
When Shutdown occurs, the Demolisher gunner must wait til its nearly over then load himself into the gunner seat while the lone Chopper ferries the first launchee back to the Demolisher to take over gunning duties. It sounds complicated, but mastering the gunner/launchee dance should be easy for two skilled players.
For 25-man mode, the following vehicle breakdown is recommended.
4 Siege Engines
5 Demolishers, two of which have a single permanent gunner and three of which have two players each doing the launch dance. The tactic for this on 25-man is the same as on 10, accept instead of one vehicle doing it, three are.