A simpler solution might be to change the position of your main lights. Looks like they're currently aimed right at both the subject and the background. Bring them more to the side and angle them away from the background. A white panel at the base of the sitting bench angled up a bit will provide fill. It might even provide a more pleasing light as it will have some direction to it depending on your power levels for each of the lights.
I think you'll struggle with this lighting position to flag the background sufficiently to keep the main light off of the entire background. A flag would most likely block only the sides, leaving the spill light still hitting the center of your fabric.
You can test this by shooting an image without the background gel light firing. You'll see instantly how much of your main light is hitting the background.