Kit
Middle English: from Middle Dutch kitte ‘wooden vessel’, of unknown origin. The original sense ‘wooden tub’ was later applied to other containers; the use denoting a soldier's equipment (late 18th century) probably arose from the idea of a set of articles packed in a container.
wiktionary
From Middle English kyt, kytt, kytte, from Middle Dutch kitte(“a wooden vessel made of hooped staves”). Related to Dutch kit(“tankard”) (see below). The further etymology is unknown.
The transfer of meaning to the contents of a soldier's knapsack dates to the late 18th century, extended use of any collection of necessaries used for travelling dates to the first half of the 19th century. The further widening of the sense to a collection of parts sold for the buyer to assemble emerges in US English in the mid 20th century.
A short form of kitten. From the 16th century (spelled kytte, kitt). From the 19th century also extended to other young animals (mink, fox, beaver, muskrat, etc.), and to a species of small fox ("kit-fox"). Later usage (for other animals) perhaps influenced by chit.
16th century, perhaps from cithara.
Borrowed from German kitte, kütte (circa 1880).
etymonline
kit (n.1)
late 13c., "round wooden tub," perhaps from Middle Dutch kitte "jug, tankard, wooden container," a word of unknown origin. Meaning "collection of personal effects," especially for traveling (originally in reference to a soldier), is from 1785, a transfer of sense from the chest to the articles in it; that of "outfit of tools for a workman" is from 1851. Of drum sets, by 1929. Meaning "article to be assembled by the buyer" is from 1930s. The soldier's stout kit-bag is from 1898.
kit (n.2)
"small fiddle used by dancing teachers," 1510s, probably ultimately a shortening of Old English cythere, from Latin cithara, from Greek kithara (see guitar).