As suggested, you might wanna dual spec if your gunna pvp (can't tell if your wearing pvp gear or not, you have 418 resilience which for dungeons and raids that's 418 of a useless stat) as the traditional pve spec isn't that great in pvp, especially at lower gear levels. At higher gear levels it can give you insane burst but it still lacks survivability compared to other specs. Of course your gear could be what you've randomly picked up along the way, and that's fine, just know that you want to get rid of all that resilience for pve.
Telling you what rotation to use and explaining why are 2 different things, so I shall explain.
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My rotation is SoC > CoA > Corruption > Immolate > Chaos Bolt > Incinerate > Shadow Bolt > Conflagrate > Searing Pain.
With your new spec on adds you rarely want to use SoC, as your a fire spec RoF will usually do better. On bosses CoD is better than CoA because CoD uses 1 global cooldown while CoA uses 2.5 global cooldowns for the same time, the damage from both curses is about equal, but you can get off another incinerate or something by saving those global cooldowns. As destruction corruption isn't really that powerful, the only time you should be casting it is if your on the move and can't cast your regular spells. Shadowbolt shouldn't be cast at all as your main source of damage is fire, with the spec your using shadowbolts damage is fair, but the cast time is long and you gain no benefits from it, so casting that instead of your normal spells will lose dps. Searing pain shouldn't be used on a boss, the point of searing pain in pve is to grab aggro, it's something you use if you see a random mob on the healer.
This leaves you with Immolate, chaos bolt, conflag, and incinerate, your main spells. As twird said, you use a priority system going CoD >immolate > conflagorate > chaosbolt > incinerate. What this means is that if CoD can be cast, cast it, if CoD is on cooldown and there's no immolate on the target cast Immo, if Immolate is already up cast Conflag if off cooldown, chaos bolt if off cooldown. If everything is on cooldown and immolate is up cast incinerate.
CoD gets you the most damage per cast time, that's why it is your first priority, Immolate buffs you Chaos bolt & Incinerate damage and lets you cast conflag, so while it's damage is low if it's not on the target first you lose damage from all your other spells. When ever conflag/CB come off cooldown cast those with Incinerate as filler. Practice on a test dummy, that's why they're there, to figure out your timing.
I noticed you copied Jeno's, however if you are gunna raid you'd be better putting 3 points into suppression from soul leech until you get your hit capped. In dungeons you are fine, but for raid bosses (this goes for level 60/70 bosses as well, anything with a skull instead of level) you have a 17% chance to miss the target. As of right now you have 280 hit(10.67) which means you still have 6% chance to miss a boss. A boomkin or shadow priest will put up a debuff giving you another 3% if you have them in your raid, but even then your still missing 3% of your spells. With suppression you'd be only .33% away from the cap. I here people say that 6% isn't important, this is wrong. What if your immolate misses? Will you notice that it missed and spend time casting it again or continue on with your rotation with your spells doing dramatically less damage? What if you conflag misses? You lose the lowered cast time of you next 3 spells. Every time a spell misses not only do you lose the potential benefits of that spell or waste the cooldown, but the time casting the spell gives you 0 dps, that cast was completely pointless, you could have been jumping up and down in circles and got the same effect.
The best, and first thing you should be working on for raids is your hit. 447 hit is 17%, however with suppression or if you always travel with a boomkin or Shadow priest you only need 368 (14%) and if you have the talents and a boomkin or Shadow priest you only need 289 (11%).
As far as gear goes, you can get stupidly good gear from emblems and the ToC 5-man. Seriously, it's stupid how good of gear you can get, I know because it's the gear I have. Due to my schedule I very rarely raid, but when I do I can keep up with the other dps even though I only have 4 raid drops. Looking at my gear I'm the person elitist hate, at least until they raid with me.
This is my armory, aside from the neck, wand, trinket, and ring you can get all of this through emblems and the ToC 5-man. Just run the daily heroic every day and then whatever other heroics you want for emblems, you can gear up very quick nowadays.