I don't know of research on this, but here's my experience:

For burned fingers, thaw some frozen milk in a shallow dish, but leave it
quite cold even with some frozen pieces in it. Soak the sore fingers (arm,
etc) in the dish. The cold milk is very soothing, and the growth factors,
SIgA, and other milk components are very healing.

If you only have fresh warm milk, put some ice cubes in it to chill it and
follow the same instructions. The live white cells in fresh milk are
especially healing, and fight any bacteria present on the skin or in the
wound.

I think it helps to leave the wounded/burned area in the milk as long as the
child will sit still.

Linda J. Smith, BSE, FACCE, IBCLC
Bright Future Lactation Resource Centre
Dayton, OH USA
http://www.bflrc.com