I wouldn't divide the plants until fall. Generally speaking, it's not a good idea to divide plants while they are still blooming. They will do so much better if you put them in the ground now, let them finish flowering and establish a root system. When cooler weather comes back, you can dig them up and divide them then by cutting the plant in halves or thirds. Make sure you use a sharp knife, and sterilize the blade with rubbing alcohol before you cut. This will help prevent viruses and fungus attacking the plant when it is most vulnerable.
Depending on what variety of phlox you have, many varieties self sow. The common varieties that you find at your local greenhouses are usually hybrid phlox that have been bred for a certain color. They are usually propagated by cuttings to retain that desired color. When hybrid phlox varieties self seed, the plants that grow from that seed will usually not be the same color. Not really a bad thing, it will give you a a little variety of color, even if they won't be as brightly colored as the original plant. If I may suggest, try growing native phlox- Phlox drummondii. In my opinion, they are superior to hybrid phlox, keep their colors much better, and come in a gorgeous array of color variations. They are also super easy to grow from seed. They also spread much quicker than hybrid phlox.Good luck!
On the subject of creeping phlox..are they in bloom or done? If done you could take them out of their pots and check to see if there are several stems in various parts of the pot. If there are, you could let dry alittle then will be easier to break apart. If you happen to break any stems just stick them in the ground and keep them moist, they will sprout new roots in no time, give em a few weeks, then a light tug to see if there's any resistance, if so they have rooted, if not stick that stem back in the ground. They truely are a very easy plant. When I do spring cleanup, I brush the mat of phlox hard to get all the old crud off and if I happen to break any stems they go back into the ground to root, thus more plants... Hope that helps... Oh also, as the mat gets larger, you will find that many stems have rooted to the ground, thus more plants to spread about, just break any stem that keep he two plants together.