I washed my DD1s as it got to the stage of bin or risk the wash - wiping down was no longer an option.
They washed up ok, looked good but stopped flashing. Every now and again they flash for a little while and then die out.
Depends how much the flashing means to you both
Ds1 once threw up on his flashing lights trainers and I had to put them into the washing machine. The lights still worked afterwards, and I have subsequently washed dd's trainers in the machine too and her lights still flash, but I wouldn't rely on them working afterwards!