Is gas flow always compressible? From Franz Durst's Fluid Mechanics: An Introduction to the Theory of Fluid Flows:

When a fluid element reacts to pressure changes by adjusting its volume and consequently its density, the fluid is called compressible. When no volume or
  density changes occur with pressure or temperature, the fluid is regarded as
  incompressible although, strictly, incompressible fluids do not exist.

So, strictly speaking, although the fluid is always compressible is there a case where gas fluid flow maintains constant density?
 A: At the steady state, the density of a flow will be constant. That's tautological.
Fluids like water can be treated as incompressible because its response to a pressure change is negligible for most practical calculations.
For more information see here.
A: For "normal" gas flows, you can only have a constant density if the fluid pressure is not changing (assuming constant temperature).  Unfortunately, fluid flow requires a pressure drop, so as a gas is flowing down a pipe, the pressure is decreasing, the gas volume is increasing, the density is decreasing, and the gas is slowly accelerating down the pipe as a result.
There may be a theoretical way to increase the gas temperature at the correct rate as it flows down a pipe, such that the increase in temperature causes an increase in pressure, and a corresponding change in density profile such that density remains constant.  However, this would (again) interfere with the pressure drop required to maintain fluid flow, so the answer appears to be "no" for this question.
