You can use the Banamine (Flunixin) orally and it's onset is almost as quick as if you gave it IV. I just squirt some over their grain and have never had a horse refuse it. I rarely use Bute anymore, but do give it IV, not oral route, for one thing it tastes NASTY. If you're willing to learn and your vet is willing to teach you, I'd have the vet teach me to give Banamine IV as it was designed. If you're squeamish or not confident that you can do an IV, stick with oral.
You definitely don't give these meds IM. If the horse gets Clostridium (C. Difficile) it is a nightmare for both the horse and the owner. Can be antibiotic resistant and just takes forever to clear up and leaves a nasty scar when you're done.