Will hill runs make me faster in flat races?

Definitely. Running up, and down, hills is a great way of building leg strength in a dynamic way, meaning less time in the gym not running.

The stronger your legs are the more force you can generate with each stride. Speed requires a fast cadence, which can be improved by running downhill and also requires a good technique, which by be developed by running both uphill and downhill, as you must use your muscles in a more co-ordinated way.

Increased dynamic leg strength will help to make your muscles more resistant to fatigue, and as a result more resistant to injuries.

So there you go, find a hill, run up it, run down it, repeat. Easy!