How long after a flea bites does the spot go away?

Depends on early Rx. Treating flea bites promptly with cool compresses, 1 % hydrocortisone/calmine and perhaps an oral antihistamine (claritin/zyrtec) and tending to the scar after the lesions heal will minimize their appearance. If they are severe, exfoliation, moisturizing, sun block and over the counter anti scar treatment (mederma/neosporin scar solution) are starters for fading the scars.