Is it possible to program an ESP8266 12F using an Arduino Nano?
Yes, you can program it with Arduino but its a bit complex that way. You will need a separate Linear Regulator with Adjustable Output to get it hooked up with the Arduino.
 Its way better to have an FTDI adapter to program it.

But if you still want to know, there is a tutorial below,

Upload Bareminimum sketch so that no program is running on the Arduino.