My daughter, from 3-4 years old, could use a Neti Pot.
She uses it whenever she is sick... she gets sinus issues just like my Husband.
It greatly helps.
But you have to use it properly and per the directions.
Post-nasal drip, is irritating and causes coughing.
You could give him Kids Claritin.
It is an antihistamine and dries up the mucus etc.
My Husband who always has sinus issues... uses the Neti Pot regularly and Claritin.
Flonase, is a corticosteroid based spray.
It only, reduces inflammation. NOT cure... the illness or mucus.
It reduces, stuffiness.
Not mucus production or secretions.
That is why... the Flonase did NOT help your son.