Since it occurs when the vehicle is moving and not when stationary; the problem is probably vacuum related.
There is supposed to be a check valve in the vacuum line where the A/C refrigerant lines go thru the firewall. The check will close off the vacuum in the lines going to the A/C climate control damper actuators.
You will need to start tracing out the vacuum line looking for loose fittings or cracks in the vacuum lines.
The picture below will assist you in tracing out the vacuum lines.
View attachment 543413