DVT detection by ultrasound (when there is already a DVT installed) is already pretty efficient, because you don't need to know flow volume for that. We test it by the compression test, where a blood clot will prevent squashing of the vein when pressure is exerted on it with the ultrasound probe. Furthermore, the shape of veins is usually far from circular, making our method less than optimal.
Our method is geared towards vessels which have enough pressure in them to constrain them to a circular shape, namely arteries, but also (most likely) great veins. So it could actually prove useful not in DVT, but to detect one of its deadly complications: pulmonary embolus. Apart from this, knowing the flow passing through the pulmonary arteries would prove extremely useful in many cases. It would have to be tested, though. I cannot be sure that it works in this particular case.