Will this series of reactions work to produce potassium phosphate?
Getting phosphoric acid by heating ammonium phosphate probably won't work since it requires temperatures above 200°C where phosphoric acid will start to vaporize and decompose.

A better approach might be the reaction of ammonium phosphate with potassium carbonate. The ammonium carbonate formed by this reaction decomposes at much lower temperatures (> 60°C). However, heating will produce corrosive, irritant and toxic products (ammonia, phosphoric acid, phosphorus oxide), so I do not recommend doing such experiments.