Seriously go for Samsung note 4. Although I use HTC one m8 and I am enjoying my Chess
The best phone for chess

One with a good size screen. Samsung note 4 or Iphone 6 plus. If you think those are too big, then try a Samsung Galaxy S6 or Iphone 6. I prefer ios to android, but I've used both, and both are good. If you use the chess.com app, there's very little difference between the android and ios versions.
My "work" is offering to buy me a new phone and they asked me what my preferences are. The only thing I really care about is access to chess.com. It's a non-profit organization so I don't want to over spend, I just want be in touch and play chess. Anybody have any advice for my best choices?