To rant, to speak or write incessantly and/or rabidly on some relatively uninteresting subject or with a patently ridiculous attitude or with hostility toward a particular person or group of people. "Flame" is used as a verb ("Don't flame me for this, but..."), a flame is a single flaming message, and "flamage" /flay'm*j/ the content.
Mark L. Levinson says, "When I joined the Harvard student radio station (WHRB) in 1966, the terms flame and flamer were already well established there to refer to impolite ranting and to those who performed it. Communication among the students who worked at the station was by means of what today you might call a paper-based Usenet group. Everyone wrote comments to one another in a large ledger. Documentary evidence for the early use of flame/flamer is probably still there for anyone fanatical enough to research it."
Usenetter Marc Ramsey, who was at WPI from 1972 to 1976, says: "I am 99% certain that the use of "flame" originated at WPI. Those who made a nuisance of themselves insisting that they needed to use a TTY for "real work" came to be known as "flaming asshole lusers". Other particularly annoying people became "flaming asshole ravers", which shortened to "flaming ravers", and ultimately "flamers". I remember someone picking up on the Human Torch pun, but I don't think "flame on/off" was ever much used at WPI." See also asbestos.
It is possible that the hackish sense of "flame" is much older than that. The poet Chaucer was also what passed for a wizard hacker in his time; he wrote a treatise on the astrolabe, the most advanced computing device of the day. In Chaucer's "Troilus and Cressida", Cressida laments her inability to grasp the proof of a particular mathematical theorem; her uncle Pandarus then observes that it's called "the fleminge of wrecches." This phrase seems to have been intended in context as "that which puts the wretches to flight" but was probably just as ambiguous in Middle English as "the flaming of wretches" would be today. One suspects that Chaucer would feel right at home on Usenet.