Can using ammonia and bleach together clean a clogged drain?

No but you will be creating ammonium chloride which is a lethal gas that can kill you! Usually the reason that a tub drains slowly is that there is hair caught in the drain just below the strainer or pop up depending on what style you have. By removing the strainer or pop up, you can access the area directly beneath and remove the hair with a small screwdriver or other implement.

Baking soda and vinegar work for SLOW, but not actually plugged drains. Ammonia and bleach are not only toxic, but are more likely to destroy the pipes than clear the drain.

Mixing bleach and ammonia will do nothing to clear a blocked drain but, it will make a very toxic gas that can be very dangerous. never mix bleach and ammonia together

Mixing bleach and ammonia can kill you! Don't do it!

don't think about it! buy a small bottle of liquid plumber, cheap. it will work.