I guess you shall coordinate the time of flushing and washing. Call a plumber ASAP. Happened to me once

Plumbers are who you call not FML lmao

I wonder how old that house is

That escalated quickly.

Get rid of one lol

I am a service plumber/drain cleaner, so figured I'd respond to this one. Most likely you mean by "flooding", that there is either water coming up from your floor drain, or your toilet overflows. Either one means that the main line leaving your house is mostly blocked. Either a solid object has fallen in there - or you've got tree roots. Roots are by far the more common problem. If you have a large tree in your front hard(or back depending on what state you are in), then 95% chance that's your problem. Other types of blockages will typically block your line 100% where it will not drain at all. I suggest calling a plumbing company that does a free line camera inspection with a cabling, so you know for sure what you're dealing with. If it's roots and you don't have a 4" outside cleanout- a cabling will only temporarily fix the problem, it could come back very quickly. A Hydroscrub, on the other hand, will completely clean your line, and should last for 5-10 years. A hydroscrub should not cost more than 1000 regardless of where you live. There is a rare possibility your line has mostly collapsed as well. If that's the case, you could be paying 6000-14000 depending on what city you're in and how deep it is.

Tounce trolls

Could be that your drain wasn't sized properly as washing machine and toilet both carry a big load. But also could be a blockage. Get a plumber to camera your drain to see.