Just out of curiosity;
1. What's the basis for your definition of slow reflexes?
2. How do you know what reflexes are required, how do you gauge them, and how are you comparing yours against that level?
As far as developing reflex skills, there's different things out there.
Physical: repetitive activities requiring hand-eye coordination. Some athletes use something like this:
http://www.activeforever.com/p-1442-quick-hands-bola-trainer.aspx
Personally as a goalie, I like tennis balls and walls. It's cheap, and simple.
Mental: Improving cognitive brain functions. Sites like luminosity have different activities online geared for this. This is where stuff like video games can help, but you need both the mental and the physical.
However, considering that you are considering joining the army ;D I would suggest you not focus so much on reflexes and more on what you require to join; administratively and physically. Lightning fast cobra hands won't help you if you can't run to where you need to use them.