I'm not sure about thickness, and I've never tried to build mudflaps, but the styrene I use for scratchbuilding is Evergreen....and they have bags of strips, tubes, and sheets for a decent price in a large variety of sizes(around $2.00-$3.00 per bag). If your LHS doesn't have them, I think you can order direct, as I have no idea where you could order some. The website is:
http://www.evergreenscalemodels.com/