Free Falcon. It's set in Korea. It's realistic too. Yes it's free.
Thread here for download link
http://www.subsim.com/radioroom/showthread.php?t=177256
Objective accomplished
Edit: Just realized that you mean first Korean War. Well I don't know any but if second Korean war erupted Free Falcon would be it :-)
Until then it may not be historically accurate but nonetheless a realistic flying sim and fun too and I must add good looking.
And I'd like to second Wings over Vietnam. It's a lot of fun especially when heavily modded.
If the purpose is to get the feel of Korean era planes such as Mig-15/17/19 then I'd also suggest Wings over Israel. Heavily modded too will give a lot of fun and it's also a gorgeous game to look at well maybe except the terrain.