I was trained to use file cards, and "picks", but I have used a piece of brass plate stock once, and it worked well for me- as Roy describes.
Years later, cleaning out my Dad's shop, I found a long piece of copper plate that he had put electrician's tape to form a better handgrip. When I examined the working end, you could easily see that he was using it to clean files. Why he didn't show us that trick I will never know.
Not everyone has access to flat brass, or copper plate. But, if you visit a scrap yard, its something to ask about, and buy. Lots of uses for the home gunsmith.
Oh, I tried using Aluminum flat stock for cleaning files, and it didn't work well. I believe its simply too soft to do the job well. An aluminum plate(1/4") under a bottom pour casting pot works great, as it transmits heat so fast, that any lead that drips on it, or spills, cools very quickly, and hardens for easy removal.
Final thought: The Best way to keep your files cleaned is in preparing the file before you use it. Fill the grooves with chalk. The chalk prevents metal from getting down and Sticking hard to the teeth, and is easy to remove with any form of scraper. Re-chalk the teeth. The chalk also keeps the file dry and free of rust between uses.