We home inspectors see accordion style flimsy flex duct over and over again on dryers and air-handling equipment. I would say that it is present in 90% of homes that I inspect. In newer homes it is often a short length behind a dryer. It does not go through the wall but connects to smooth metal ducting that takes the exhaust through the crawl space. However, in older homes, and some that are not so old, I have seen the flex duct leave the back of the dryer and run through the wall and about 20 feet to the outside. That is a real no, no. Often it is broken and the crawl space is full of lint. Duct tape and flex duct seem to go together. This flex duct, being easy for the homeowner to twist and bend, has found its way into use in air handling or exhaust ducts, such as bath fans. Once I saw a homeowner use it for an honest to goodness heat duct from the furnace.
Fact is, doubly so for dryers, flex duct is not a desirable product. It is pretty obvious that the ridges will collect lint and look at the sag in the duct below. This collected lint is probably more prone to causing damage to the dryer, as it overheats, than causing a fire -- but that could happen as well. Personally, if it is a short length, used as a connector, I tell people the facts. If it is a twisted concoction like the one below, that is coming apart and all taped together, I suggest an immediate upgrade to smooth metal ducting.