I'm just about as anti flex duct as they come, but I do think this is a reasonable way to do it. It uses it where it's strengths are. I used to do HVAC design and this was common and good practice there, from a properly sized branch system, with flex from the ends to the diffusers.

As the whole duct run, as is common in residential, it's no good. It falls into the realm of things that while theoretically possible to do well, just require a level of diligence and effort that aren't going to happen the vast majority of time.