Freezing cooked chicken
I've frozen cooked chicken & turkey and had no problem with it tasting different. I just put it into a freezer bag like CaliforniaSunshine and freeze. You can lay it out on a lined baking sheet and freeze it then put it into the bags so that the pieces will be separate and easier to just take what you need instead of having to thaw a whole block that you might not want to use all at once.
I think it really loses texture, therefore quality, if you freeze chicken after it's cooked.
But sometimes, you have no choice. Better that than letting it spoil or throwing it out.
I've found the best method is to freeze it in stock. Think about those ancient woolly mammoths that explorers find encased in glacial ice that have been perfectly preserved for thousands of years.
I put it into a ziplock or plastic container with enough stock to cover. If I don't need the stock when I defrost the chicken, I'll use the stock for another purpose within a day or so.
You can't really tell the difference if you're going to use it in a casserole or something with a sauce.
I do it all the time! Divide into portions, wrap in cling wrap, place all into a freezer bag, press out air, and freeze. I wouldn't keep it frozen more than a month. We make chicken salad, add to soups and casseroles. Best way to defrost is in the fridge overnight, or use defrost feature of a microwave.