What states of matter can flow?
Liquid and gas
The particles are further apart for both, which allows them space to move around easily. The properties of matter can be break down using the table below.
Actually, all of them can flow, its just that liquid and gas do it more easily.
Even solids can flow, they just do it much more slowly - the rheological phenomenon of "creep" whereby solids undergo extremely slow deformation over time at stresses far below their critical yield stresses illustrates this.
There are certain types of synthetic polymer which look and behave like rubbery solids, but if left for extended periods of time will slowly "creep" to take the shape of their container. For other types of solids the rate of creep can be so small as to be almost immeasurable. For crystalline solids it is effectively zero.
So the answer is that all states of matter can potentially flow, but liquids and gasses do so the most readily,