$NaC{l}_{\left(aq\right)}+AgN{O}_{3\left(aq\right)}\to AgC{l}_{\left(s\right)}\downarrow +NaN{O}_{3\left(aq\right)}$  is a redox reaction.

There is no change in the oxidation number of atoms in reactants and products. Hence, it is not a redox reaction.

Note: In redox reaction both oxidation and reduction are taking place.

There is no rule to produce vapor when solids or liquids burn in a flame.