Yup! "Brand" also means fire. It's used when describing large fires, such as when buildings or ships burn. I'm guessing that's why it's called a brandmand, since they are meant to put out larger fires, and not simple 'ild'. It declines like this: En brand - branden - brande - brandene. Compare this to the Danish verb 'burn' - at brænde.
A burn (the injury) is called a "brandsår" literally a "burn-wound". You may also encounter the word "ildebrand" - a "fireburn" (or a firefire) which is the same as a brand, but a very childish way of saying it.