Help :(

You could try raw aloe saturated wraps around the legs.

 

I burnt the heck out of my hand once, and in desperation, chopped an Aloe Vera plant open and held it on my hand. Total relief. Try that with the chick by rubbing some Aloe Vera gel on the burn. Make sure the bird is warm and put vitamins-electrolytes in the drinking water. You may need to apply it a few times a day. Let us know how it works.

I have to ask. How did it get burned?

 

If you have plain neosporin you could put that on it tonight. You can give Baby Asprin (80 mg) to chickens but, you will need to cut it into quarters for a chick. You could then smash it and then divide that 1/4 in to two doses for a baby chick. You can give it to it couple times a day, just put in hard boiled egg mash or plain yogurt.
Do Not Give Chickens Advil, Tylenol or Ibuprophan - They are Toxic !!! And No topical pain killers that end in or have "caine" in the name! Poor Baby hope it gets felling better soon.