How to prevent the washing machine outlet from backflowing to other devices
If these appliances are supposed to drain into a standpipe, then they need to be connected in a way that allows them to drain in open air. 

Get a double wye, of the appropriate size to fit on the standpipe.  Then put one drain into the left wye, the other into the right wye, and leave the center wye open. 

If the standpipe opening is large enough to accommodate both drain lines, and still have open space to "breath".  Then you should just be able to put both drains into the standpipe, without adding any other fittings.