You can use "Tom will be washing clothes" in two possible contexts: 1) By itself, it means an arrangement that Tom has made, as far as you know (you might have to ask Tom again later). 2) When paired with another future action, it means Tom's action will already be in progress when the other action happens.

I learned a rules that means: When somebody is doing something right now you may use to be verb + verb (action)+ing When somebody will do something after some minutes, you can use just will verb + verb (action) in infitive form. But I'm sure both are right

Tom is washing the clothes. (continuous) Tom will wash the clothes. (future)

Wshing is a noun. Wash is a verb. Both sentences mean the same. To use the noun form, washing... the verb needed is "be".