What is the value of a limited edition Kennedy half dollar?

There are no true "limited edition" Kennedy halves. The Mint doesn't make "limited editions" (with that name) of standard coins.

My guess is that your coin is in some way altered by a private company, e.g. by gold-plating it, or perhaps is one of the lower-mintage years that's been put in a special package.

If it's plated, that destroyed any collector value it may have had. The only good thing would be if the coin was dated earlier than 1971 because it would contain silver - 90% for 1964, 40% for 1965-70 - so you could at least recoup that much.

If it's something else and is in a special holder there are some niche-type collectors who may want to purchase it but it's not really of interest to most mainstream coin collectors.