Is "First Aid" capitalized in a sentence?

No it doesn't have to be unless if you are referring to it as a proper noun but in this case, "I got out the first aid kit and handed it to dad."

It really depends on the context.

If you are using it in a noun phrase - first aid kit - you don't have to capitalize it. But, if you are saying - Certified in First Aid, then you would capitalize it, because it is the name of an assistance.