S., I'm an exercise physiologist specializing in prenatal and postpartum fitness. You should get the OK from your physician at your 6-week appointment before exercising. Other than the incision healing, a C-Section is not all that different from a vaginal birth as far as the damage that has been done to the abdominal region. You would still probably have a "belly" after 5-6 weeks regardless of the C-Section.
I don't usually like to disagree with other advice on this site, but exercise does not decrease milk supply. Dehydration can decrease milk supply, so if you are exercising you'll want to increase your water intake (which you should do if you're breastfeeding and you should do if you're exercising anyway).
A couple of things that you can do immediately to help are posture improving exercises. A lot of the damage that's done to our belly's is actually related to the alignment of the body being compromised during pregnancy and postpartum. The weight of baby and breasts pulls the body forward as does bottle feeding, breast feeding, carrying the baby, pushing strollers, etc.
What I always have my postnatal clients begin with is sitting on a large resistance ball and squeezing their belly-button tight into their lower backs and then releasing. You can do this exercise sitting in a chair or standing, however the ball will keep you from slouching. If you're standing or sitting without the ball, make sure you keep your chin and chest up and sit up straight. Stretching your chest is also important and fine to do now. A great way to stretch the chest is to stand in a doorway with your arms on either side, elbows level with your shoulders and wrists above the elbows. Keeping your chin and chest up and shoulders pressed down, gently walk through the door until you feel the stretch across your shoulders into your chest. Hold for 30 seconds.
You can also go for walks. Make sure you keep your posture straight while you're walking, particularly if you're pushing a stroller. Keep your chin and chest up, your abs sucked in, and your butt tucked underneath you.
Once you get the OK, start slowly, especially when working the abdominals. You can actually do more harm than good if you don't work them properly. Oblique work puts the most stress on the damaged areas, so you want to make sure you build up to those. Pelvic tilts are a good starting point and then add very controlled curls while keeping your chin up and belly button pulling into your back.
Good luck and I hope this helps. There's a lot more information, but this is a good starting point. I actually offer a class that runs for 6-weeks specifically for this topic, so this is really just the tip of the iceberg.