Is home synthesis of cellulose acetate possible, and why?
The bottom line is that this would be a very bad idea to try due to safety reasons alone, and is not realistically feasible using only household materials regardless.  

Glacial (100%) acetic acid is dangerous if not handled properly and requires an appropriate fume hood at a minimum. You also are not going to get to glacial acetic acid from vinegar, and water will kill this reaction.  

Acetic anhydride is a reagent that you just won't be able to obtain or synthesize yourself. Even if you did, it would be hydrolyzed by the water in your impure acetic acid.  

Sulfuric acid is commonly used as a catalyst, and while you could obtain this, it should absolutely not be handled by someone without appropriate equipment and training in it's safe usage.  

So again, this is just not a feasible project and there would be serious dangers along the way if you tried. I like your creative thinking process and I hope you will pursue some other, safer, home science project.