Do you mean flashing used in roofing? Copper is a soft, ductile metal, flashing is particularly so and is thin for easy bending to conform to corners. I expect you'll have a problem with denting if you use it. If you really want to use copper, then get something thicker and harder than pure copper. I'd take a look at Beryllium Copper alloys since they are both harder and resist corrosion.
There's also the issue of cost and availability. I would expect to pay around $100 a square foot for 1/8" copper sheet, more for a sheet of Beryllium Copper alloy.
I'd recommend using aluminum instead. It is widely available in a number of sizes and thicknesses. I would use 1/8 or 3/64 sheets to resist denting. This page
from The Metal Store online catalog shows you the price of various sizes of 3/64" smooth aluminum sheet. 24" x 36" x 3/64 is under $30.00 US, while the same size in 1/8" (the thickness of aluminum deck plate) is $67.00 US. The metal store is just an easy-to-find example from Googling. There are lots of other places to choose from -- doubtless some are cheaper than this.