Making sure to breath down and supporting your breath with your diaphragm, rather than to the chest, and not to exhale all your air at the same time is extremely important for anything that requires use of breathing. This is called 'breath support' or 'full breathing'. If you're doing it right, you should feel your stomach inflating when you breath in, rather than your chest.
A few exercises to help you work on breath support include:
- Hold your hand in front of your face with your palm facing you. The blow each finger after full breathing, as if they're birthday candles and they won't go out. Make sure that when you exhale, you direct all the air towards one point (finger tip) rather than just letting the air escape.
- Take a full breath down to your diaphragm for 4 counts as you can (make sure not to breath into your chest!), hold your breath for 8, then make a strong 'hissing' sound for 8 counts. Over time, as you get better, increase the amount of counts for all three of these things.
If you feel like either of those exercises is too easy, then try doing it while lying down on your back.
Now when it comes to actually rapping, don't try to hold all your air in. Know your raps well, and know where to snag a quick full breath - this becomes especially important with faster raps.
As for thinking about breathing making you lose concentration - the only way to solve this, is to practice, and then practice some more. Eventually breathing properly and at the right time will become something that you can do without thinking about it.