Generally, having windows by the fireplace is not a problem. Our fireplace works extremely well even in extremely bright rooms with lots of windows. When viewed from the normal viewing position, say several feet away on a couch, you will not see any reflections of windows.
The only time you may see a reflection is if you’re standing within a few feet of the fireplace and looking down on the glass. The illumination in a bright room will do little to diminish the flames as they will still look bright and vibrant even in a room with a lot of windows.