How can I power an ESP8266 using a 9V 1A barrel connector power supply?
You cannot. If you look at the datasheet:

https://cdn-learn.adafruit.com/downloads/pdf/adafruit-feather-huzzah-esp8266.pdf

you can read all details on page 25/26:


  Alternative Power Options
  
  The two primary ways for powering a feather are a 3.7/4.2V LiPo
  battery plugged into the JST portor a USB power cable.
  
  If you need other ways to power the Feather, here's what we recommend:
  
  
  For permanent installations, a 5V 1A USB wall adapter (https://adafru.it/duP) will let you plug in a USB cable for reliable
  power
  For mobile use, where you don't want a LiPoly, use a USB battery pack! (https://adafru.it/e2q)
  If you have a higher voltage power supply, use a 5V buck converter (https://adafru.it/DHs) and wire it to a USB cable's 5V and GND input
  (https://adafru.it/DHu)
  
  
  Here's what you cannot do:
  
  
  Do not use alkaline or NiMH batteries and connect to the battery port - this will destroy the LiPoly charger and there's no way to
  disable the charger
  Do not use 7.4V RC batteries on the battery port - this will destroy the board
  
  
  The Feather is not designed for external power supplies - this is a
  design decision to make the board compact and low cost. It is not
  recommended, but technically possible:
  
  
  Connect an external 3.3V power supply to the 3V and GND pins. Not recommended, this may cause unexpected behavior and the EN pin will no
  longer. Also this doesn't provide power on BAT or USB and some
  Feathers/Wings use those pins for high current usages. You may end up
  damaging your Feather.
  Connect an external 5V power supply to the USB and GND pins. Not recommended, this may cause unexpected behavior when plugging in the
  USB port because you will be back-powering the USB port, which could
  confuse or damage your computer.