Yes, phlox are very very easy to propagate.
All you need to do is either split the plant or take a cutting.
The splitting can either be done in the spring or early autumn, with the early spring a slightly better time.

Get a sharp spade and literally 'chop' a section of plant off if it's a large clump and replant straight away in a new spot.

If not, cuttings can be taken at this time of the year.
What you need to do is find a shoot with not obvious flower buds forming on it and then with a sharp knife or pair of scissors, cut off a length of about 4-5" , then trim it off just below a pair of leaf joints.

Next is to prepare some potting compost mix for the cutting.
I use around 2/3 of multi-purpose compost to 1/3 sharp sand mixed throughly.
Then all you need to do is pop your cutting into a 3" pot or into a 'cell tray' so around 2" of the cutting is below soil level.
You can use hormone rooting powder if you want, that will help speed up rooting and ward off damping off and rotting.

when you have done a few cuttings (always do more than you need to allow for losses) take the pot or tray with the cuttings in, and place in a propagator or use some clear polythene to make a tent to help keep the humidity up and raise the temperature a bit and leave somewhere with good bright light , but not full sunlight and keep the compost moist but not wet and with any luck you should have rooted cutting within 2-3 weeks!!

Phlox are one of the easier cutting to take so don't worry

hope this helps?