I actually work at an industrial fabric company. We have all sorts of different types of fabric like that.
Keep in mind that a wrinkle (texture) free background can be achieved with lighting. Wrinkles show up as texture because a directional light will cause shadows behind the wrinkles...but if you add more light, from another direction, you can fill those shadows...and if there are no shadows, it will likely look smooth in a photo.
Honestly, paper is probably the easiest wrinkle free background. You just have to keep in mind that it's a consumable product. When it gets dirty or destroyed, you just roll out more...and when the roll runs out, just get another one.
Another option would be to build a solid structure like an infinity wall. Basically you use something to create a curve where the floor & ceiling meet. Then you can finish it and paint it white (or whatever).