The best covenant for Fire Mage is Night Fae for both Mythic+ and Raid.
Night Fae’s signature ability, Shifting Power, provides the cooldown reduction needed along with kindling to make Combustion a 1-minute cooldown.
The other ability, Soulshape, provides more mobility to an already extremely mobile class.
When the full tree is unlocked, go for Niya or Korayn for the damage increase.
Otherwise, play Niya with 2 potency or Dreamweaver with 2 potency. At the start, Dreamweaver will provide you with two potency conduits early on.
Soulbinds and Conduits
Single Target: Infernal Cascade + Discipline of the Grove
Cleave(M+): Infernal Cascade + Discipline of the Grove
Infernal Cascade increases your fire damage when you use Fire Blast in Combustion for 5 seconds.
Discipline of the Grove is the highest DPS increase for a second conduit as it provides more cooldown reduction when using shifting power.
The finesse conduits to go for are Flow of Time or Grounding Surge.
Flow of Time reduces the cooldown of Blink.
Grounding Surge reduces the cooldown of Counterspell when you interrupt a target.
Use any of the 3.
Fevered Incantation is the best Legendary for Mythic+ and raiding. Its a really nice passive damage increase, currently the highest DPS.
It's really important that a Fire Mage uses the PvP Badge trinket. It increases your primary stat on a one-minute cooldown, which makes it have incredible synergy with Kindling and Shifting Power.
As for the second trinket you can use Soul Igniter, Unbound Changeling, Cabalists Hymnal or Insignia from PvP. Soul Igniter sims the highest for single target but the other trinkets are good for Mythic+ and AoE.