A gas flows from an area of high pressure to an area of low pressure when there are no other forces preventing it. From a macrosopic perspective you have to infer that an underlying force is accelerating the gas towards low pressure.
The following animation shows a container filled with air which is at first divided by a barrier in the middle. Both sides have the same temperature but the left side has two times the density of the right side and thus has a higher pressure.
When the barrier is removed, more molecules move from high pressure (left) to low pressure (right) than from low pressure to high pressure. This creates a net movement of molecules towards low pressure which is macroscopically measured as a gas flow. The important part is that the molecules do not move into the low pressure area because they are accelerated by an underlying force; they statistically move there due to their thermal motion. Molecules statistically move where is less resistance by collisions which is generally towards an area of lower density or lower temperature.
The pressure-gradient force seems to accelerate a gas at the macroscopic scale but there is no underlying force that accelerates molecules. In my view the pressure-gradient force is an entropic force; it does not exist at the microscopic scale. It results from the system's tendency to achieve thermodynamic equilibrium which is based on the molecules’ thermal motions tendency to bring the system toward its macroscopic state of maximum entropy.
What do you say?