The simple answer is that you can't but that's not quite the whole story.
If you want to continue to use Win32 API calls like
SetConsoleDisplayMode
then you're going to need a Linux implementation of Win32. The best known of these is
'Wine Is Not an Emulator'[
^]. This will give you what you need.
Another alternative is to change your code ( assuming it's all console based ) to use the NCurses library. This does all the Console realted stuff you could want and is part of the Linux Standard Base ( i.e. available in every distro ). It's also available on Windows as PDCurses ( Public Domain Curses ). Using this approach would give you extremely portable code that could be built for almost anything from Android to Windows to OSX.