I haven't yet researched this, but here are my first thoughts:
A mammogram is just a fancy X-ray that involves alot of squishing. The theoretical danger of radiation is that too much of it can mess up your DNA. Your body has enzymes to repair the damage, but they can be overwhelmed if you receive too high a dose. The amount in a mammogram is far, far, far below this limit. And regardless, it absolutely should not do anything bad to the milk you're producing.
My bigger concern would be that the mammogram wouldn't be able to get an accurate read of your breast tissue, and so wouldn't be worth very much. Remember that the purpose of a mammogram at this age is twofold:
1. To look for any problems (and unless you've got a family history, the risk of your having a serious problem at your age is pretty tiny.)
2. To give a baseline image to compare to future mammograms, when you're older and the risk of problems will be higher.
Since your breasts are going to look different on a mammogram when you're lactating, it's not going to be able to act as a baseline for future mammograms. If you're going to go through all the discomfort of a mammo, it might be best to wait until you're done lactating to avoid confusing people!