In all honesty, the very best thing you could put on it right now is manuka honey.
It's a strong, dark, caramel honey from New Zealand (from the flowers of the manuka tree) and it has around 20 different kinds of antibacterials identified in it so far. So it's a strong antibiotic - in the UK they use it to fight MRSA infections now because it works where other antibiotics won't. It also keeps the burn moist so it won't dry out and promotes safe healing without scarring. I've used it on grease burns before and there's not a scar or mark to be seen, and they healed really fast.
The Maori have used it for centuries for cuts/burns/scrapes/wounds etc, and here in New Zealand it's a very common cure-all remedy for any ailment you can think of, including colds, flu etc.
Just put it on the burn and cover it with a band-aid or plaster or bandage or whatever.
http://news.bbc.co.uk/2/hi/health/3787867.stmhttp://www.naturalnews.com/023670.htmlThe second link is about a company making products with it in the US, if that helps... the honey itself is only found in NZ but you can get it worldwide now in health food shops and supermarkets. It tastes great too.
Hope that helps!
Manuka is good, so is most honey. I will grant you kiwis that Manuka has been shown to be somewhat stronger against particular bugs, but regular stuff works pretty well, also.