I have two questions: First, how can I make my own iPhone scratch removal kit? Second, how do I remove scratches from an iPhone?
If you do find a method to remove scratches, and since the screen would no longer have any of the protective coatings left on it, definitely get a screen protector to help reduce the chances of the screen scratching again. You could opt for an oleophobic screen protector to reduce the fingerprint smears that would be left on the screen with normal use, but you may be better off buying a new screen and replacing the screen or glass. Depending on your region, you can find replacement screens for pretty cheap (I have seen them for $25USD from time to time).
Although it is harder to scratch the screens on most phones today (at least the bigger named brands with specialized glass), there is always the chance of getting scratches. This is the main reason I apply screen protectors on my devices, and recommend others in doing the same thing. It is cheaper to replace decent screen protectors from time to time than it is to replace screens.
Primarily it depends on the iPhone, further it's questionable whether you should try it in the first place.
For example the iPhone 4/4S has both the front and back out of glass. Trying to removing scratches from glass is a tough if not pointless, even for surface only scratches. On top of that pretty much anything you use on it will remove the oleophobic coating meaning you will have lots of finger prints and smirks on it in the future.
The iPhone 5/5S has glass in the front and the back is primarily anodized aluminum plus a special ceramic glass at the top and bottom. Technically you could polish the aluminum however doing too much will reveal the natural color of the aluminum and metal processing requires some knowledge and skill.
Every scratch is different and quite frankly, none of the "known" methods is foolproof and will work every time. It's make or break...