Unless you are using pipe and fittings that have been sitting around and turned brown, it doesn't take long to clean them. Like HJ said, if you are having problems putting it together, something isn't round or there is a raised edge from cutting the pipe. If the edge of the pipe is raised, try using a file to bring it down to size.
Sometimes fittings become dinged at the edge were the pipe is inserted (happens more on bigger fittings when they are dropped on a concrete floor). Up to one inch, you can smack the opening with the ball end of a ball pein hammer to make the it round again. (you aren't hitting them real hard because you have to hold on to the fitting). Often, it is not worth the trouble to straighten small fittings. It cost more in time than the fitting is worth.
There are tube fitting brushes without handles that will fit in a drill. But it won't save much time. They only work inside the fittings. Also, the handle of a normal tube fitting brush can be cut of and used in a drill, but the brush doesn't last as long as the others. If you are cleaning tons of fittings, this can save your wrists.
I have worked in a shop doing pipe fabrication. Sometimes one person would clean and flux while another solders (piece work). Flux wasn't left on overnight.
Nocorrode also turns pipe green. Excess needs to be cleaned-off after soldering