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1866, represented as typical of American English, perhaps from jam (n.) on pattern of shivaree [Barnhart]. For the second element, Weekley suggests French bourree, a kind of rustic dance. Klein thinks the whole thing is of Hindu origin (but he credits its introduction to English, mistakenly, to Kipling). Boy Scouts use is from 1920. Noted earlier as a term in cribbage:
Jamboree signifies the combination of the five highest cards, as, for example, the two Bowers [jacks], Ace, King, and Queen of trumps in one hand, which entitles the holder to count sixteen points. The holder of such a hand, simply announces the fact, as no play is necessary; but should he play the hand as a Jambone, he can count only eight points, whereas he could count sixteen if he played it, or announced it as a Jamboree. ["The American Hoyle," New York, 1864]