I was going to post about this Shebeest jersey when I saw the above. This jersey looks like a nice polo, but in wicking material and the zipper pocket is nice and flat. I just wore it for a ride to the farmers' market, where I had my purse in my pannier, so I didn't need to stuff my pockets.
I have one or two wicking tees that have a very teeny zip pocket on the side seam, maybe big enough for a license and a dollar bill. I think they are by Mountain Hardware. Also, look at Athleta running stuff. I am pretty sure their running tops have something like this.
2015 Trek Silque SSL
Specialized Oura
2011 Guru Praemio
Specialized Oura
2017 Specialized Ariel Sport