I'll give you my input on the matter and hopefully help you improve your dps
You need the Fevered Incantation legendary. Gives you a nice boost to your overall damage and is especially strong during combustion. Make sure to socket this with haste and versatility missives.
You need Infernal Cascade and Discipline of the Grove (this is from the Night Fae covenant only) conduits, Hopefully you're Night Fae, considering they offer the best damage output for fire mages. Venthyr could be considered, especially if you're an active pvp player and do high rated content, but if you're not, go Night Fae. There are other conduits that could be useful in specific cases, but these are the two to go with for most pve content.
You need Sinful Gladiator's Badge of Ferocity. This is a pvp trinket with a base ilvl of 200 that costs only 700 conquest. To increase its ilvl, however, you need to do rated pvp content and reach certain brackets:
1400 - 207
1600 - 213
1800 - 220
2100 - 226
If rated pvp is something you're good at and you can get to these brackets, great! Otherwise, get at least the 200 version of it. This is a great trinket because despite having crit as the main stat, it gives you intellect on a 1 min CD, which you can line up with combustion (more on this later). Besides this trinket, you should try to get Unbound Changeling (MoTS dungeon), Soul Igniter (Sun King in Castle Nathria raid) or Inscrutable Quantum Device (DoS dungeon).
You need haste. Lots of it! Haste and versatility are your main stats as fire. Haste because it gives you shorter CD fire blasts, allows you to spam more spells during combustion and helps you get combustion back faster, and you should aim for at least 20 %. Versatility because it makes you tankier and boosts all your damage, including that from external sources such as trinkets and Shifting Power (Night Fae spell).
Although crit gains value because of the legendary effect, you have 100 % guaranteed crit from several perks of the spec (combustion, searing touch talent..) so is not as important. Mastery is just not worth it at this point and should be avoided as much as possible.
Lastly, because combustion is where most of your damage will be coming from, you need to get the rotation right. You can find several guides and youtube videos explaining it, so I recommend you check them and practice it on dummies, as it can take you some time to get it right.
You can find some variations to the rotation, so I'll give you the one that works for me and that allows me to maximize my dps.
Pre-cast pyroblast around 3 seconds before pull. Around 80 % of the cast, pop combustion and 2 fire blasts (both fire blasts must be cast before pyroblast lands on the target). Because it's not possible to use your trinket/ racial/ pots while you are casting pyroblast, I have my combustion macro'ed to include them.
Below you can find the full opener:
Pyro - combustion (at 80 % of the cast) - fblast - fblast - combustion (to activate trinket, pot and troll racial) - pyro - pyro - phoenix - pyro - fblast - pyro - phoenix - pyro - fblast - pyro - phoenix - pyro
As a reference, at 22.35 % haste (what I have) I almost miss out on my last pyroblast. This is why not only haste is important but also activating combustion as late as possible when you are hard casting your first pyroblast. Because pyroblast has a travel time, make sure also that you standing 25 to 35 y away from the boss (not too close but also not at max distance).
Note that for subsequent combustions within a single fight, you should replace the hard cast pyroblast by a fireball. No need to spend almost 4 seconds hard casting it at this point.
In dungeons, where aoe is more prevalent, my combustion rotation is as follows:
Fireball - combustion at 80 % - fblast - fstrike - fbast - phoenix - fstrike - fblast - phoenix - fstrike - dragon's breath - shifting power (fblast while combustion is still up to extend Infernal Cascade buff). Outside combustion, basically hard cast FS on 2 or more targets (if you have Flame Patch on), and cast fire blast while hard casting to proc instant flamestrikes, for example:
Cast flamestrike, during the cast, 2x fire blast, when flamestrike ends, cast the instant one.
Note that hard casting flamestrike is only worth it if the adds are not constantly moving out of your cast area, out of flame patch, and if you don't have to constantly interrupt your casts to move around (I usually just shimmer to avoid stopping the casts).
I think this covers the main aspects of fire and hope it helps you on your progression!
My armory link: https://worldofwarcraft.com/en-us/chara ... /timepiece
My crit is 28 % and not 13 % as displayed on the armory.