To get the flags you first need to beat the game than do the following.

Unlockable	How to unlock
Alvida pirate flag	Beat Alvida in 1-1 then find her in 6-1.
Arlong's pirate flag	beat Arlong a second time around.
Black cat pirate flag	Beat kuro the second time around.
Buggy's pirate flag	Beat buggy the second time around.
Cook pirate flag	get sanji and talk to Chef Zeff in 4-1.
Kreig's armada	Beat Don Kreig the second time around.
Navy flag	beat axe hand morgan or chaser the second time around.
Red hair pirates flag	Beat boss battle mode in all difficulties.
Straw hat pirates flag	get all the flags but the red hair pirates flag.
Veggie pirate flag	it's behind the veggie pirates in 3-1,you have to have Ussop to get past them.