Nitrocellulose (flash paper) synthesis without Sulfuric Acid?
I do not think it will be possible to form nitrate esters of cellulose without sulfuric acid present, I am sure that you need the strong bronsted acid to make the reaction work. But I think that there is another issue here, your safety / health / the law on energetic materials.

I hate to have to say this, but I do not think it is safe to make energetic materials using nitric acid at home. You should also consider for a moment the question of "is it legal" to make the energetic material at home.

Keep in mind years ago some "home chemists" would make explosives / fireworks and it was regarded as "boys will be boys". But nowadays the "boys in blue" (Police) are very keen to chase after people who make explosives / things which go bang etc.

I think that the distillation of sulfuric acid at home does not sound like a good idea, I think that you would need to work in a good fume hood. Most school labs would be unlikely to have the equipment required to do it.

With all due respect I think you should choose another chemical project to pass the time while you are on "lockdown".