Q: My iPhone 6 will not allow me to unlock my phone. Emergency Calls only screen. Any help?

Use your passcode to open the device from that emergency screen.

Then it seems your passcode is incorrect. You can try a reset. Hold the sleep/wake and home buttons together until you see the Apple logo and then release. The phone should reboot. See if you are able to enter the device then. If it will not accept your passcode, then you need to restore the device. See this support document for help with that. Forgot passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple Support

Follow the instructions in the support document that I provided that say, "Use these steps if you have an iCloud account and have Find My iPhone turned on".

Remove it from the Find My iPhone account.  Then restore in iTunes.

So you went through these steps:

Find My iPhone

If you enabled Find My iPhone through iCloud, you can use it to erase your device.

1. Go to icloud.com/#find.
2. If prompted, sign in with your iCloud Apple ID.
3. Click All Devices at the top of your browser window.
4. Select the device you want to erase.
5. Click "Erase [device]" to erase your device and its passcode.
6. Use the Setup Assistant on your device to restore the most recent backup.

and it is just showing the logo flashing on and off?  According to this support document, If your iOS device restarts, displays the Apple logo, or powers off while you're using it - Apple Support  if you experience this behavior, contact Apple support. You can make an appointment at the Genius Bar of the Apple store nearest to you or Authorized Apple Service provider, depending on your location.