Creation and Combustion of Nitrocellulose
Flash paper is commonly used in classroom demonstrations, I think, and it is made of nitrocellulose.  A journal article from 1995 describes rapid creation of flash paper through nitration with nitric acid.

I have never done this procedure myself, but looking through it the biggest safety risk to my eyes is using and handling concentrated nitric and sulfuric acids.  $\ce{H2SO4}$ and $\ce{HNO3}$ are very dangerous especially when concentrated.  Full PPE when handling these is an absolute must.  I'm glad to hear in your question that you are already thinking about safety requirements at this step.

Another important risk is the inherent risk of lighting anything on fire.  Nitrocellulose is an energetic material.  Since it is heavily nitrated, it needs less oxygen gas to completely burn than things like wood, paper, or even gasoline: a lot of oxidizer is already built into the molecule.  This risk is best managed by only ever igniting small quantities of nitrocellulose, and of course by storing any larger quantities of the nitrocellulose far away from sources of ignition.  Full PPE is a good idea too.  Perform the combustion in a well-ventilated area.

I'm less worried about the particular risk incomplete combustion forming dangerous levels of $\ce{NO_{x}}$, especially if you limit the combustion to small sheets of nitrocellulose at a time.  High levels of $\ce{NO2}$ are unlikely to form via incomplete combustion; if large amounts did form, since $\ce{NO2}$ is a strong oxidizer, it would react with remaining nitrocellulose to less toxic, more reduced nitrogen oxides or more likely to nitrogen gas.

Small amounts of $\ce{NO2}$ do form from high-temperature combustion of anything in air, but if you use small amounts of flash paper, exposure of your students to $\ce{NO2}$  is likely to be background sources in the atmosphere will vastly exceed anything produced by your demonstration.

All that said, don't take too much safety advice from the internet.  Talking to experienced chemists in person who have done this demonstration is probably the single best thing you can do to stay safe.

Update: I should explicitly say that although I have never made flash paper, I have burned small pieces of it on numerous occasions, never with any problems or even noticeable amounts of smoke or fumes.