Is a back flow valve needed to attach a washing machine?
One way to accomplish this is; You can add one Inline spring check valve to each supply line. 

After the check valves you can tee the hot and cold together with one 1/2" copper pipe out into a 1/4 turn valve  and then to the correct threaded piece to accept the washer supply hose. 

The check valves will prevent water from one pipe from pushing into the other. 

To regulate the temp of the water you could use 1/4 turn valves BEFORE each of the check valves and close them partially to adjust the temp of the water.

Or just plumb in mixing valve made for the job of mixing and not allowing back flow. I have seen shower mixing valves used for washing machine supply in older homes.