Does flow affect the amount of water in the flow meter?

The initial amount of air can vary depending on your fill flow rate. Then it will be affected by your pump pressure, the higher the pressure, the less air that will be visible (as air is compressed under pressure). Typically, you can evidence this, between when the pump is running, and when the pump is off.  Over time, the air dissolves back into the water and will naturally disappear, as it is absorbed into the water.