I used to have 2 roller shades on my double windows without issue. Just make sure they get cut to the exact proper width.

If it were my house I would likely do two pull down shades. Yes, light is going to come in the gap, so the room will not be pitch dark, even with black out shades.

Which way do the windows face? Light coming in the sides is much more of a problem when the sun is beaming in the window versus being on the other side of the house. I lived in a house with a west facing bedroom and had blackout cellular shades. They were fine in the morning, but during an afternoon nap, sometimes a beam of light would hit me square in the face.

You could add a second layer with blackout curtains, but you would have to leave one drape open during A/C season.

I'm not picturing what you mean when you say the frame is flush with the windows. Do you mean with the glass or the trim (if you have trim).
Can you inside mount the shades? If they're measured and cut correctly, there shouldn't be a gap. But not sure how your windows look.