As you are using the PSoC® 4200 Protoyping Kit (CY8CKIT-049-42xx) Are you running it over the USB power or are you using 3.3 Volt supply? Also what model of ESP8266 are you using and have you programmed it? I have found that this device can be affected by USB signals.
Yes, I'm using the kit that You mentioned. I'm running it over the USB power, but I've made some wire that lowers the voltage from 5 V to 3.3V not to damage the ESP, so my kit has a 3.3 Volt supply that way. I haven't programmed it, right now I'm thinking about upgrading the firmware, because from what I can see right now there is a version from 2013, so it could also be a cause of this problem. Also I was connecting this ESP to the USB port directly via some device, don't know how it's named in English, let's say its USB adapter and it's working fine. The problem is only when I connect it to my PSOC 4