While there are a lot of people who might say things like 'a good BLM knows when to save their procs' and such, generally what these people mean is 'I'm awesome and I have nothing to contribute other than to insult you by saying that what you're having trouble with is easy'. Saving your procs amounts to getting one, knowing that you'll have to move within the next 5 seconds, and casting fire I first because you know you can squeeze it in before you move and use your proc then. It's pretty much never going to be a good idea to hold onto a firestarter or thundercloud for more than 1 or 2 casts. Hell, it's not like they last very long to begin with.

You're probably over thinking it. Just use your procs as you get them (not cancelling to use or anything). If you find yourself in a situation where you get a proc and know that you will have to move very soon then go ahead and save it for that, but more often than not you'll use procs while moving only if you just happen to have them, not because of any intent.