I have a "back flow" situation. My washer drained into my kitchen sink then It must have clogged completely. It overflowed above the line that drains into (main drain) into kitchen.
How do I fix this. I think this house has multiple plumbing problems.

"I think this house has multiple plumbing problems."

Then you start with the worst problem and work back.

Snake the line out from the kitchen sink roof vent. Put out enough cable to reach the base and 20 feet more. Test and flush the line by cycling the washer. Good luck, Tom