ESP8266-01 not working: red LED barely lit after reflashing from FTDI board
You are trying to power the ESP8266 from the on-board regulator of the USB-serial converter, who is not able to supply the current required to actually run the ESP8266 WiFi. (You might be able to run an application on the ESP8266 that doen't enable the Wifi).

Use a 3.3V supply than can provide at least 400 mA.