There are always 5 red chests, two of which can randomly spawn in alternate locations.
Location 1 (Red Chest)
Near the big dumpsters outside the room with the vending machines. This chest randomly spawns in an alrternate location on top of the stairs in the jail room, near the north door; see the map.
Location 2 and 3 (Red Chests)
Inside the room opened by Claptrap as a reward for completing the Claptrap Rescue: Crimson Fastness mission.
Location 4 (Red Chest)
Inside the "Eat Skag and Die" cell in the jail. If not spawned here, it can be found right next to the chest #5.
Location 5 (Red Chest)
Near the exit to Crimson Enclave and the garage with the Lancers. The chests can be seen through a chain-link fence but cannot be reached when the garage door is closed. The garage door will only open after the Badass Defender wave has spawned. The Badasses will spawn when the opposite door is approached from either side.