Look at the fabric. Nylon fabric is shiny, whereas polyester looks a bit like cotton.
Feel the fabric between your fingers. Nylon feels lightweight and is water repellant. Polyester is heavier and feels like cotton.
Watch how the flag flies on the pole. Nylon flaps in the slightest breeze, but polyester flags are heavier and take much more wind to carry it aloft. In heavy winds, the light nylon fabric will "snap" loudly, which is why people prefer using polyester flags in windy areas to reduce wear and tear on the flag.