Since the bill of a cycling flap is all flopsy, I don't think putting it through the washing machine (and line drying) affected mine in the slightest. I've only done it once though and it's wool if that matters at all.
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Bikes: 1996 Eddy Merckx Titanium EX, 1989/90 Colnago Super(issimo?) Piu(?), 1990 Concorde Aquila(hit by car while riding), others in build queue "when I get the time"