It looks like it uses the psu from your phone, right?
If so Im guessing its not enough for all your Zeroes peripherals.
you need to get a proper powered hub with a 2A psu minimum, you need that just to power the Zero, never mind the extra stuff. Are you booting to the desktop? Are you seeing a rainbow square in the top right corner of your screen?
That means your psu is too low powered.
That thing you got looks like its only for phones.
Pi 2 running LibreElec Krypton, Pi 2 running Wheezy Desktop, Pi 1 headless Wheezy, downloading Radio, Pi 1 running Picore headless Media Server, Pi Zero to be an Old Time Radio Project. Pi 3 testing. Pi Zero W downloading Radio shows headless.