This weapon consumes an incredible amount of ammunition, as a single slight burst consumes 3 flamer fuel instaneously. It has no 'warm up time', such as its counterpart, the rapid-torch flamer, and the residual flame does 8 damage per second for 5 seconds.
The slo-burn flamer can be found on the upper level of the southeast portion of the launch platform base inside the Enclave mobile platform during the Who Dares Wins quest. It is on a platform with deathclaws that are in stasis fields. It is in 100% condition when found.