Flashing ESP8266 over WiFi whith samrtphone? I'm working on a project in which an ESP8266 is the brain of the device. I want to add new features to the device controller later but this requires that the user open the controller and reprogram the ESP8266.

I want the user to be able to update the firmware with his smartphone (maybe through an application). How can I do that? Is this possible with this chip?
ESP8266 OTA can be performed through a web browser as detailed in the ESP8266 OTA information page.

Since a smartphone has a web browser I can see no reason why you can't use that.