If you have liquid, we know that Lugol's has a shelf life of about 10 years, so it seems to me SSKI shouldn't be any different, when sealed and kept in the dark. It might need some shaking if the solution has separated, though I've never had that problem.
It sounds as though you might have tablets. Here's what the American Thyroid Association says:
"KI is made in pill and liquid forms. The two FDA-approved brands of full adult dose 130-mg KI pills are IOSAT® (Anbex, Inc.) and Thyro-Block® (Medpointe, Inc.). The FDA-approved brand of 65-mg KI pills is ThyroSafe® (Recip US). Properly packaged, KI's shelf life is at least 5 years and possibly as long as 11 years. If you accidentally take a very old pill, it may not work fully but it won't hurt you."