Yes, you can find a flag that will perfectly fit into the flag holder at many hardware stores. You will need a flag with a thick dowel, because most of the mini flags you purchase at the store will fit into the flag holder, but have a lot of wiggle room. This will bring forth potential hazards as your kid could remove it and become injured from the tiny, thin dowel.
You will need to find a flag that is approximately 18 to 24 inches tall because the dowel is usually thicker. Having a thick dowel will provide a snug fit and prevent your child from removing the flag.