I can't find コシなし defined in any dictionary. It looks like it might have something to do with udon noodles.
From goo dictionary:
この餅は腰がある This rice cake is chewy.
For noodles, 'chewy' is probably not the best choice. I've seen it equated to al dente in English and that is probably a better translation.
コシなし would be the opposite, what we might call soggy noodles in English.