Like your work. How can I be of help?

Fill me in on a few things, like 35mm, 6x6 or larger?
The type of flash you have and do you have any accessories for it, or are willing to create some.

Flash might be nice to paint light with inside some of these locations but do not stray away from the natural light look too much.

So, if you are using a 35mm camera you have shutter sync issues to deal with if you are doing fractional speeds. Some cameras sync at 1/125 or maybe 1/200 (the shutter is open all the way when the flash fires, else it leave a black band from the closing shutter curtain). Shooting long exposures does not have this as an issue. Open camera shutter, fire off flash, close shutter.

Shooting with copal or other iris type shutters in the lens can be synced at any speed, but again the issue is not a factor on long exposures. So it really comes down to how you want to paint light.

In your image on the left, there are shadows caused by natural light. If you were to up the light in the room you will want to think about where you place the light so shadows look good. The light from the flash will help elevate the light level but hopefully not look like a happy snapp photos from the flash.

Bare bulb flash (depending on what flash unit you have) is a nice way to evenly raise a room's light level. If you have an on the camera flash like a Nikon SB model it will not do bare bulb but you can fake it a bit with a white plastic grocery bag. Puff up the plastic bag, put it on the flash head like a bad wig, (See photos of Donnald Trump) and start with low power seting (1/28 or something like that)to throw light to all locations in the room when your shutter is open. Remember the orientation of the flash as a light source is important.

Also a flash / ambient light meter is a nice tool. It can give you the ratios of how much natural light vs. what the flash gives you. Start to use one and you will love it.

TMI, probably. Experiement, keep good notes and enjoy.