There has been backup of water in the tub, this accurs from time to time. Only in the lower level it started with the kitchen sink and now its only the tub in the lower level bathroom. Everything else works great. It does get worse when we use the bathroom upstairs and the washer next to the bathroom that we are having problems with. We have tried cleaning the pipes checking for a clog. We have poured the special black bottle liquid as instructed. What else should I check.

We have poured the special black bottle liquid as instructed.
And now you know that chemicals only work in TV commercials.
You have a partial blockage downstream from the lower bath tub. The solution would be to either snake from the downstairs lavatory roof vent, from the tub waste and overflow.(see image) or you could pull the toilet and snake from there. Let me know which way you want to go and I'll be glad to assist. Good luck, Tom