Several scientific papers study FR-PLA (fire resistant PLA) in which Aluminium Hydroxide nanoparticles are melt blended into the PLA (example source: Advances in Flame Retardant Poly(Lactic Acid). Would spraying the nanoparticles (dispersed in a liquid -source - maybe non flammable silicon oil) onto a 3D printed PLA help with fire resistance or not make a difference?
I suspect this is too late. The whole point of embedding the nanoparticles inside PLA is that it remains inside until needed (when temperatures rise above ~300 °).
By applying it as a coat, it can be easily scratched or rubbed off because PLA is so soft or flexible. You are also running into the problem of shedding of Al(OH)3 NP everywhere which may be a problem.
A coat of sprayed Al(OH)3 NP is only going to be a few micrometres thick, or you will need to use some glue to make them stick, which complicates thing and changes the appearance of your product. On the other hand, embedded Al(OH)3 NP are present throughout the entire thickness of the product. During fire, your sprayed NP might dehydrate just from the heat of radiation without even coming into contact with fire.
This is a bad solution.