I'm using the Reface DX as a master MIDI keyboard for my DAW. The Reface DX constantly spits out MIDI clock messages, is there any way to stop this?

Yes, it does. And no, there is not. The Reface DX is a device that has a clock and therefore it generates the clock message (along with Active Sensing). This should not be a problem for any DAW connected

Also, when changing programs, the Reface DX will send out Program Change messages. The problem is some DAWs, for example FL Studio, respond to Program Change messages, and the results are undesirable.

Like any MIDI device with programs it sends a Program Change when a Program is selected. Again this should not be a problem for any professional DAW. What are the undesirable results - you should contact the makers of FL Studio and ask them - I cannot think of a Yamaha product (or any other for that matter) that doesn't send these types of messages on a regular basis.

The problem is not in the reface DX... almost any device you connect will send this type of information and it should not present any issues for a receiving DAW.