I agree with pretty much what most people have been saying here. In general you never want to interrupt a cast to use a firestarter, and you can fire weave if you are really that concerned about missing a proc chance.

That said, as a blm that does 6-9 each week as a blm (without swapping to smn on some turns which is popular) fire weaving isn't always practical in all fights and all situations during combat. Some of the off GCD spells are very useful and should be held back for specific uses ( manaward to mitigate damage from briars or fireballs, manawall to mitigate meteor stream, etc) what I have been doing is using some off GCD spells or actions I won't have any need for in a given fight (lethargy and potent poisoning potions are some I commonly use to weave and will fire weave with them when they are available, if I don't have an off GCD ability or spell that I don't value for it's use somewhere else in the encounter, I still would not interrupt a cast to get out a firestarter.