I don't actually know but it's definitely a thing, a lot of patients have reported it. There's an iron infusion we give for anemia that's apparently particularly flavorful.
The best explanation I've heard is that it's basically stimulating your tastebuds/odor receptors from the inside, which implies that you're always tasting your regular blood but you're just used to it. (Further evidence: I once had a liver infection that dumped a bunch of bilirubin in my bloodstream, and besides making me yellow and generally unwell, it tasted terrible.)
In theory saline is just salt water and shouldn't taste like much, but I've tasted those flushes (the normal way, with my mouth) (I was curious) and they don't just taste like salt water, they have a weird plasticky flavor. They're supposed to be preservative-free so I don't know what that is, maybe it's from the packaging or maybe it's some ingredient that isn't technically a preservative or a "stabilizer" or whatnot.
Anyway, that's my theory - you're tasting plastic syringe off-gas from the back of your tastebuds.