For what it might be worth, I'm adding this late item to an old post, because this is where I ended up while trying to solve my own problem.
Repeatedly, I received the 7:1:9:14:4 error while re-registering an Echo Dot via the Alexa app on my Fire HD. Tried all the suggestions herein, to no avail, and was ready to call Amazon for an assist.
Before doing so, I attempted the registration from the Alexa app on my phone, and it worked perfectly, first time. This doesn't prove an error on the Fire HD, and may be simply time, chance, and circumstance. But, if you're having this problem, and have the option of trying the app from a different device, I'd suggest that doing so would be a good use of your time.