ESP8266, Vcc and CH_PD oscilation
In the future, please provide a schematic. It is very difficult to understand those awful picture diagram things.

Your issue is that you are using a voltage divider where you should have a voltage regulator. The voltage divider provides 3.3V with no load, but when the ESP draws current, the voltage drops. Ohm's law can tell you why.

The solution: use an actual 3.3V regulator, and make sure to adequately decouple it (the ESP can draw very large spikes of current, particularly when transmitting).