Closing your account is impossible, and the admins don’t respond to emails.
One of our users points out:
I have tried to close my store at IGSkins, but had no luck. Their site says on the FAQ page that they can “deactivate” your store at “any time”. I’ve sent them repeated requests to close my store, but have never heard from them. […] In short, it is impossible to close a store on IGSkins or delete your Instagrams from IGSkins.
Try contacting them via the contact form found here: http://igskins.com/contact.php