Ok... let me see if I understand what you're trying to do...
You want to copy the non-directory contents of a tree of directories... for example, given the following tree:
./a/b/file1
./a/file2
./a/b/c/file3
you want file1, file2, and file3 to be copied elsewhere without maintaining the directory structure.
You CANNOT do this with a single cp command - copying files recursively without maintaining the directory structure doesn't really make sense. Still, it's not an impossible or difficult task - you could do it in one line with find.
Code:
find DIRECTORY_TO_COPY -not -type d -exec cp -d -i "{}" DESTINATION_DIRECTORY \;
Obviously, by removing the directory structure, some files may have the same name. Using the -i flag for cp (as above) will have cp warn you if this happens. The -d flag will have cp preserve symbolic links.
See man cp.
See man find.