Ashes would require an oxidising environment. SO far as I know, the surface of the moon, with or without solar radiation, is more reducing than oxidising. I don't know how nylon would behave during long-time exposure but some sort of competition between splitting and rejoining of the long-chain organic molecules would see it approaching a tarry consistency. After bleaching the coulours out of the plastic, the plastics themselves would darken and polymerise in complex ways to leave a brittle but solid skin draped over the moon dust.

I'm sure that I can see where the flag WAS in the pattern of footprints. There's a focus at 10:00 with a clean dot in the centre. it should have been blown away radially in that direction, but no idea how far...

Just give me a space-time machine and I'll go get it back for you, Raoul...

(as a special favour, I'll take a rake and drag it around the surface to spell "Raoul was here" or "Raoul loves _______". That'll look really good in the next set of images!