Yes and no. We can measure our speed and direction of movement against the cosmic microwave background, which averages over a much larger area than our visible

Yes and no. We can measure our speed and direction of movement against the cosmic microwave background, which averages over a much larger area than our visible Universe (if redshift is interpreted as light aging because of ether), but local measurements will be sensitive to local flow only. It's like measuring speed of wind to calculate position. It's possible, to some degree, if you have a map of winds, but its precision is extremely low.