So, I was reading the New Space Marine codex, and saw how the Legion of the Damned is a add-on army now
This threw me what codex are you reading? My 5th edition codex says they are an elite choice not an add-on army. My apologies if I misunderstood your statement.
I to run a derivative of the Salamanders and have had some issues. Like the guys who are the most into flame throwers and melta's do not have widest variety of weapons of that nature. The actual chapter that has the widest variety the Blood Angels for some damned dumb ass reason (if your unfamiliar they also get pistol versions of flamers and melta's). Disregarding that as you mentioned Devastators can not carry Heavy Flamers.
If you are looking for a more salamander feel to your army I would use sternguard with Heavy Flamers instead of legion of the damned. From what I have read it fits better with the Salamanders. Not trying to be a fluff nazi here just my personal opinion. The Salamanders are some of the best weapon smiths out of all the Space Marine Chapters they craft and care for there own weapons over centuries. Salamanders also have not spawned a single successor chapter in the 10,000 years since the Horus Heresy (at least none they have ever officially documented). So saying there troops are a bit rarer and thus more expensive than your typical Ultramarine knock off is an understatement. Sternguards with there increased attacks, better moral, weapons options, and ammo variants just talk more to the salamanders the fact that they can carry combi's as well since those are described as hand crafted combinations of different weapon types.
I agree with you as I am not a fan of the 5th Edition Space Marine Codex with its watered down chapter individualism. I have long said to the folks in my gaming club that they were 6 pages short of finishing the codex. There should have been an alternative rules page for each of the 6 1st founding Chapters/Legions covered in the book (Imperial Fists, Ravenguard, Salamanders, White Scars, Iron Hands). They could have simply set up the Ultramarine rules as the standard and said if your going to make an Imperial Fists chapter (or founding off of a Fists chapter) you replace chapter tactics with this, heavy bolters cost 5 pts less etc etc etc.
P.S. However keep in mind if I remember correctly in 4th edition the variant rules for the Salamanders actually allowed them to be the only chapter to carry Multi-Meltas. Even though I think this is the most useless heavy weapon to put in a devastator or tactical squad it will add a Salamander feel to your army fluff wise.