Later tonight, the new version of 'The Flash' premieres on the CW. Because there was already a version on CBS back in 1990, this Scarlet Speedster will be found in the Land O' Remakes. Barry Allen, aka The Flash, will now be played by Grant Gustin, but in a nice "Shipp O' The Hat" to the original series, the first Flash - John Wesley Shipp - will have a recurring role as Barry's father Henry.
Because it's in the Land O' Remakes, that means any episodes of 'Arrow' in which Barry Allen appeared will also be in that alternate TV dimension as well. However, for the most part, the 'Arrow' we see is taking place on Earth Prime-Time otherwise.
It may be that 'Arrow' is the first series to alternate episodes between dimensions like that on a regular basis. There have been shows with a few isolated examples (like 'Batman' with three dimensions worth of Mr. Freeze.) But on the whole, there's been a clean break between the dimensions we see and there's no viewing back - like 'Alias Smith And Jones' (due to the recasting of Hannibal Heyes) and 'The Dead Zone' (because the show introduced a new Commander-in-Chief who was not the same POTUS as in Toobworld and the Real World.)
Besides the tip o' the hat in casting Shipp, 'The Flash' is bringing on board Amanda Pays from the original cast. And even more Toobworthy, she'll once again be playing Dr. Tina McGee!
Not every character in the Land O' Remakes has to be recast. Because this Barry Allen was born decades after the original from Earth Prime-Time, his spin of the wheel in the telegenetic lottery made him look different from Shipp's Barry Allen.
But that doesn't mean Remake Tina McGee couldn't have been born at the same time as the original. More importantly, she must have been conceived under the same circumstances so that they are cross-dimensional twins. (As as you should know, despite the original series being cancelled after one season, that world's Tina McGee lived on in Earth Prime-Time.)
The temptation was there to claim that this "new" Tina McGee is actually the "old" Tina McGee; that for some reason the Flash brough her through the dimensional vortex (a trick he could do in the comic book world by the vibrational shift of his molecules at high speed or something.) But the series hasn't even premiered yet and I won't interfere in the unfolding of their storyline in such a way. (Post cancellation, a TV show becomes fair game for speculation!)