The story
Uncertain, but likely from the filler syllables boom-laka-laka-laka in the lyrics to the song “I Want to Take You Higher” (1969) by Sly and the Family Stone, which appeared as the corruption boom-shaka-laka-laka in subsequent covers; the modern shortened form boomshakalaka, as an apparent reference to “I Want to Take You Higher”, appeared in the military comedy film Stripes (1981). From there, a scriptwriter for the video game NBA Jam (1993) adopted it as onomatopoeic for a slam dunk in lines voiced by Tim Kitzrow, popularizing its use.
Etymology from Wiktionary, CC BY-SA 4.0.