A thin, sharp crackling sound.
Late 16th century; earliest use found in John Dee (1527–1609), mathematician, astrologer, and antiquary. Alteration of crackling, probably with imitative motivation, the higher vowel being intended to convey a sharper cracking sound.
That makes a succession of thin, sharp sounds; that crickles.
Late 19th century. From crickle + -ing.