I've read that the superior AOE (area of effect, used for multiple enemies) rotation is:

FireIII > FireII x 3 > Flare > Convert > (FireIII at first mp regen tick > FireII x 2 > Flare > Convert) repeat actions in parentheses.

Basically, FireIIs are a bit more effective over time due to their consecutive damage compared to the slower Flare, but you still want to cap each AOE rotation off with Flare. Flare spam is not quite as good for AOE anymore.

Your best use of Raging Strikes is right after using FireIII, that way you do the most Fire/FireIIs with AF3 up before Raging Strikes wears off.

Your single target rotation is fine. Which thunder you use depends on how quickly you're going to regenerate MP with UI3, since sometimes using ThunderIII will leave you waiting a second to cast FireIII again. I typically use ThunderIII if I think I'm going to be standing still for a while, but I do ThunderII on a highly mobile fight, because I want that FireIII casted and to be able to move as soon as possible. I'll also use ThunderIII when I have a Firestarter proc up, since you can quickly transpose (to buff the FireIII damage a bit) and instantly cast the FireIII.

Playing BLM becomes dynamic when you have to start anticipating the best time to use procs and swiftcasts in order to ensure optimal DPS and casting uptime. If in the middle of a rotation, it's considered best to always use your Thundercloud proc as soon as possible, as it has the potential to let you see a Firestarter proc come up just in time to use it. Also, if you do have to move to dodge mechanics, throw a Scathe in if your MP allows. It's always best to try and have outgoing damage whenever possible. ABC, always be casting.

BLM is my 2nd job, so some dudes can go in deeper, but this is coming from a dude that typically does the best or second best DPS in my groups. It's crazy how much room there is for improvement with such a seemingly simple job, that's why I love it!