Kongregate games are (predominantly) Flash-based, so you’d need a smart phone that still supports (or can be “modified” to support) Flash, in order for you to be able to play games on your phone. With that being said, mobile is being phased out. There hasn’t been any new mobile badges in a fairly significant amount of time and mobile game uploads has been discontinued.
So, it’s not a good idea to get your hopes up that you’ll be able to play Kongregate games on your phone. As well, it’s kind of silly to buy a phone with the intention of using it for one thing (besides calls, and if that’s your plan).