Check out this discussion for some thoughts (including mine):
Hopeful future Burn Nurse
How did *I* start on a burn unit? I was a new grad, I wanted to start in an ICU, my local teaching hospital/level 1 trauma center hires new grads, I applied, and they hired me. I live in a state where an ADN is all that's required, though we're encouraged to get a BSN. I live in a relatively low-income region...I think a lot of people put in a few years in the ICU and head off to CRNA school or whatever they've been dreaming of. That wasn't ever my goal (not that there's anything wrong with it) and I've stayed with my unit since I was hired.
Personally, I'm not sure I would have "made it" as a floor nurse. I think it would be great experience, but I'm grateful I didn't have to go that route. Burns in my hospital fall under the overall auspices of the Surgery department (vs the Medicine) department, so I'd guess that starting on a surgical floor (if you can't or don't want to start in an ICU) would be helpful. You'll probably get a good number of wounds there, too--surgical wounds, ostomys, infected chronic wounds, etc... I don't actually think that burns are very similar to any other wounds like the type I mention above--you'll need to learn the burn assessment and wound care practiced at the center where you work, but the surgical background will still help you.
My hospital didn't require any certifications (other than BLS) when they hired me. They have all their ICU RNs become ACLS certified after a few months of practice, and they have all the Burn RNs do the ABLS class (which, honestly, is more designed for hospitals that don't have burn units, but it's a good class). We're encouraged to pursue further degrees, get our CCRN, etc... I will point out that I'm not in an ABA-verified burn center, but we do take patients from a large geographic area. My unit only cares for adults, but pediatric burns go to the children's hospital and are managed by the same surgical team.