"a sudden burst," 1827 of an argument; 1858 of light, from verbal phrase; see flare (v.) + up (adv.). It seems to have had some vogue as a street expression in London in the 1830s.
Flare up! flare up! is all the cry, in every square and street —
No other sound salutes your ear, whoe'er you chance to meet
Where'er you ride, or walk, or sit, or breakfast, dine, or sup,
They welcome you or quiz you with "Flare up, my boy! flare up!"
[Fraser's Magazine, April 1834]