Obviously, their portfolio of past work is the best start. Although a designer can adapt their style to meet the needs of each client, you should see a design identity across the realm of their work. Does their past work *look like* the kind of work you are looking for in your brand identity?

A logo and an app icon are *very* different things. From a process perspective, if they suggest designing both the logo and the icon at the same time, they are inexperienced and should be avoided. A good designer should first want to iterate the logo in black & white without text. Once the logo, typeface and colors have been locked, then an app icon can be designed that is pixel-perfect.

I would suggest looking through Dribble to find someone with a great portfolio that includes app icons.

Happy to talk through this in a call if you need more clarity.