Icon design experience
Just because you’re an amazing illustrator doesn’t mean you know how to create an icon. In addition to looking at overall quality, designer have to have experience with digital design and specialized in app icons.
Professionalism
Of course you want someone with design skills, but you also want an icon designer who listens to your needs and gets work done in a timely manner. So take past customer experiences into account to make sure app icon designer will make all aspects of the design experience seemless.