I've never seen this usage, and spin-off is generally used for TV shows, but can it also be used for comic book based TV shows? For instance, Barry Allen was first seen in Arrow.
Yes and no.
The Flash was introduced as a back door pilot on the Arrow. They introduced Barry on The Arrow as a way to gauge interest in the production of a new show. This makes it a spin off.
But a spin off is typically done with a supporting character of a show. Barry was only in one episode of the monster of the week plot of Arrow. And introduced solely as a back door pilot, so it's worth as a spin off is lessened.
Another factor is that The Flash is it's own media franchise prior to the recent tv show. Most spin offs start in one show before getting their own. The Flash was independently created, but Barry is a copy of the original Flash Jay Garrik.
Regardless of everything, the Flash is commonly referred to as a spin off, by both production and everyone else, so it is a spin off.
No, it is more a sidequel, instead of a spin-off
spin-off: media, a spin-off1 (or spinoff) is a radio program, television program, video game, film, or any narrative work, derived from one or more already existing works, that focuses, in particular, in more detail on one aspect of that original work (e.g. a particular topic, character, or an event).
sidequel: spin-off may be called a sidequel when it exists in the same chronological frame of time as its predecessor work.
Yes, it can be used for these shows, but it's not the favoured term.
Some people may not like to use the term "spin-off" here because spin-offs are traditionally seen as "lesser" shows - typically a cheap money grab on an established brand name that's either cancelled, or soon to be cancelled, after a long, successful run. Spin-offs are also not, historically speaking, expected to last nearly as long as the show they spun off from. Examples would include Joey as a spin-off of Friends or Fraiser and a spin-off of Cheers. (Although Fraiser had a pretty long run in its own right, regardless of what you think of the show.)
In recent years, the rise of the "shared universe" concept leads us to treat multiple spin-off shows as "equals" when they take place in the same setting. And, to be fair, these shows all usually launch close together and run concurrently, and they all usually have similar budgets, so that term ("shared universe") might be preferred these days.
I think it's still perfectly valid to call The Flash a spin-off of Arrow. Historically speaking, even as recently as ten years ago, this would have been the defacto term. However, I suppose it's also fair to say the term is a bit dated. At least in regards to these "shared universe" set ups. "Spin-off" could still be used, for example, to describe a show like Fuller House without much debate.
Note: I'd never heard the term "sidequel" before, personally. I agree it's an accurate term to use with The Flash and such, although perhaps not very common.