Where did the term "flame war"/"flaming" come from?

to flame OED figurative

b. Of persons: To burn (with envy, fury, indignation, etc.); to look angrily or passionately upon. to flame out, up: to break out into open anger or indignation; to ‘fire up’.

As in:

1548 N. Udall et al. tr. Erasmus Paraphr. Newe Test. I. Matt. xxii. f. 'Whiche wholy flame with enuy and hatred'.

and

1681 J. Crowne Henry VI i. iv. 49 I flame with fury to be at it.

More recently:

intr. slang (orig. and chiefly Computing). To rant, argue, or harangue, esp. via an electronic medium (such as e-mail or postings to a newsgroup); to send an inflammatory, abusive, or (esp. in early use) inconsequential e-mail or posting, usually as a hasty response or in a rapid, angry exchange. Also trans.: to send (a person) such a message. Cf. flame n. and adj.

as in:

1981 CoEvolution Q. Spring 31/1 Flame, to speak incessantly and/or rabidly on some relatively uninteresting subject or with a patently ridiculous attitude.