Iodine solutions prepared at the concentrations on the color chart should react with the paper. It is important to dip the strip the full 60 seconds. The reaction takes place very slowly.
On the other hand, the reaction of the same iodine paper to chlorine is very fast. If you have access to regular household bleach (typically 5-8% available chlorine depending on the manufacturer) you can take a tablespoon of bleach and mix it into a gallon of water. Using the test papers, the iodine strip should develop a deep blue/purple color. If it does not, then something is wrong with the test papers. If it does develop the deep blue/purple color with chlorine, then the problem is not the strips.