This sounds promising. Is there any documentation on here to get SuperSu on the Fire? It would be great if i could get this method to work. I really dont want to open the thing. Thanx for your help.You need a different root method.
I've just put Lineage 12.1 on my Fire HD10 with firmware 188.8.131.52. It was straight forward with no issues but I got the same error you did.
Instead of the root method used in this post, use SuperSu instead then come back here and carry on with the rest of the process.