Can I use a Miele washing machine for US (2 x 110V) with 220V plug
It's not supplied with 2 cords.

The washing machine is supplied with a 5’ 3“ (1.6 m) long, 3 wire cord, ending in a NEMA 5-15P plug, ready for connection to a 120 V, 15 A, 60 Hz, AC power supply.

Instructions page 84.
If you see a second cord-and-plug, it's for the dryer, which is a completely different appliance.
Your plan is not going to work for several reasons.  First, there is no way to develop 120V from a Euro style 230V supply, except by using a large transformer.  (the hokey travel adapters will not work; they use electronic trickery that will not work with a big motor load like a washer.)  Second, the power frequency is wrong, and the washer cares because it has a big motor that will now be running at the wrong speed with the wrong reactance, and will tend to overheat.
So really, you need a rather hefty electronic sine-wave inverter that would turn 230VAC/50Hz into 120VAC/60Hz, but this is not some $50 travel adapter off Amazon, it's a large multi-hundred dollar machine.
Do not ship large electric appliances across oceans.
It's a waste of fuel.  They won't work. Just sell em on Craigslist and buy replacements off Craigslist once you're there.