Probably if you can get a good schematic and a copy of the firmware. The odds of doing this are like my two neighbors slim and none. The add states " Dynasonics DFX Doppler Flow Monitor, 0.15 to 30 FPS, No Input/output" I am assuming you can find a unit with input and output. You can contact Davis Instruments and see what they offer.
The answer to your question is yes. All you need is a supplier that can write the data blurb in a sensible manner. The output is usually 4-20mA, which is commonly handled by Arduino.
Are you wanting to make the instrument yourself? If so, the difficulty will be creating a transducer or transducer pair ( I have only worked with models that have a transmitter and detector) that can make sense of sound waves reflected off of moving particles inside of a pipe that are moving at different velocities because they are at random distances from the pipe wall.
Should be an easy task. Oops sarcasm again. Truly though if that is your intent you are taking on a very difficult challenge. You do have the benefit of researching patents to find out how others have done it.