Let's start by taking off the suffixes and then we'll see what's left. The Yiddish suffix -ach indicates a plural, as in rogelach or kinderlach. So removing the -ach leaves us with koishekil (or koshikel)- and "-il" is a diminutive suffix. So koishiklach is the plural of "little koishik". But what's a koishik?
While much of Yiddish comes from German and Hebrew, there's a significant amount that comes from the Slavic languages, and this is where we find the meaning of koishik - "basket". For example, basket in Polish is "koszyk" and in Czech and Slovak - "košík" or "koš". In fact, the Yiddish translation for basketball is koyshbol.
Are there any cognates to these words in English? I think so. The Online Etymology Dictionary provides the following etymology for "chest":
O.E. cest "box, coffer," from P.Gmc. *kista (cf. O.N., O.H.G. kista, O.Fris., M.Du., Ger. kiste, Du. kist), an early borrowing from L. cista "chest, box," from Gk. kiste "a box, basket," from PIE *kista "woven container."
This seems to me likely to be the origin of kos(ik) as being a basket in the Slavic languages as well.