My understanding is that fap as onomatopoeia comes from [the webcomic Sexy Losers]
I do not know when the second p started to appear.
There seems to be some agreement that Sexy Losers at least popularized the sexual verb, whether or not it originated it — and that takes it back to 1999. Also in 1999 in Sexy Losers, the feminine counterpart, shlick (Urban Dictionary in 2004: “The onomatopoeic representation of female masturbation”).
Two examples, with the strips reduced to the final panel, and genitals cropped:
SL #158 “War Games” 10/13/02, in which guys find that long sessions of gaming can improve their ejaculation distance:
SL #166 “Psychology Games” 12/24/02, with both terms: