I'm 15 and 5'7" 3/4. My dad is 5'11 and my mum is 5'3. My ultimate aim would be 6'2" or 6'3" however my current goal is 6'.

Would this routine be useful?

Alright so far I've got something like:

Stretches in the morning and night.
3-5 minutes of kicking
100 Jumps (2X)
Hanging for 20 second (multiple times)
Cycle 30-40 minutes (if possible)
Sprint before bed
80 Sits ups
80-100 push ups

4-5 glasses of milk
6 bottles of water

Any advice (mostly on what foods would be good)

I think it's very nice man ! keep it up !

You can add this also.
Sleeping is the standing stone of a healthy body. Sleeping around eight hours every night as you grow up will have some very positive effects on your body. While you sleep your body slows down so it can rest and regenerate. If you don't, then your tissues ware down just like the parts of an engine you haven't oiled and run for long periods of time at high temperatures. Sleeping habits is one of the best tips to grow taller. What you need to do is make sure you sleep at least 8 hours each night, not day. Sleeping during the day has been proven to be less effective because there is a lot of commotion and you simply can't get relaxed enough for your body to slow down.

You must also sleep so that your spine stays into a horizontally straight position. During the day, the gravitational forces pull you down thus compressing the joints between your vertebrae. After a good nights rest, they expand into their normal position thus making you look taller. In order for this effect to be permanent, you need to get a tougher mattress so that it wont bend under your weight. Also, try and sleep without a pillow and on your back. It can be uncomfortable at first but this is crucial to getting a straight spine.