I suggest you don’t try to take out the WP_Rewrite class and re-use it in your application, but look at other frameworks instead. Many MVC frameworks have nice rewrite engines, that not only offer more flexibility in handling incoming URLs, but also generating internal links according to these formats.
The WordPress rewrite system is tightly coupled to the rest of the code, and for all the effort it would take to rip it out, you can just as easily have learned how to use a “real” framework.