The shows Arrow and The Flash take place in Starling City and nearby(?) Central City. My understanding (assumption) is that both shows are filmed in Vancouver, although each show has city shots depicting the (fictional) city where the show takes place. Arrow uses Boston for cityscape shots (no official citation, but I live in Boston and recognize the shots). What city is shown in the Flash's cityscape shots?
The Majority of the externals and locations for the show are filmed in Portland, Oregon (particularly the cityscapes).
The studios in which CW films both The Flash and Arrow are based in Vancouver, and some minor externals are filmed there as well (anything casual and unimpressive; not to sleight Vancouver, at all!).
Both shows actually construct their cityscapes from a number of stock-footage clips from cities around the world, including Houston, Philadelphia, Baltimore, Los Angeles, Frankfurt (Germany) and Tokyo (Japan).
This site has a growing list of locations that have been 'spotted' by residents.
DC/WB/CW have a lot of flexibility in creating fictional cities, and as such they can insert establishing shots that are fit for purpose. If they require a scene set in Chinatown, for example, they could simply use stock footage from a street in any number of Chinatowns across the world, or even China itself. They are not spatially or geographically bound to any sort of fidelity... so they can use whatever they have available/what they desire.
All of the Cityscapes of The Flash, as far as I have seen, I've seen every one< are shots of Portland Oregon. I know the Skyline, because I've lived there for 50 years. Its funny tho', The round Starlabs building is projected into the shots, and it jumps from one side of the river to the other in other shows.
The opening city scene (river running thru the city with several bridges over it) of The Flash series is DEFINITELY Portland, Oregon. That's the Willamette River, Downtown Portland on the left, SE/NE Portland on the right. Scenes on the computer screens and city maps in the backgrounds are also of Downtown Portland. I live and have for over 40 yrs. I always recognize the steel and glass awnings (downtown Portland, Pioneer Square, Pioneer Place, etc). It is a beautiful city with lots of very distinct landscapes, streets, buildings, street signs, back alleys, etc.
The cityscape at around 29 to 30 minutes into episode 5 is English Creek in Vancouver. You can see Burnaby Mountain in the background. The bridge in the foreground is also unmistakable.
Later, when he carries Beth out of the city by running on water, you see him run under the Lion's Gate Bridge in Vancouver. Stanley Park is at the left end of the bridge, North Vancouver at the right end.
I haven't lived there for 35 years, but those two scenes are obvious, even at this remove in time.
Google English Creek and Lion's Gate Bridge for images to confirm.