I run a Firetv Stick too. First of all, I set the default DNS to dnsforge.de (You can use of plenty adblocking DNS providers).
Second is running DNS66 as an addition adblocker, turning it on for all system apps as well and using my prefered DNS-Servers.
Then using TDUK Unified Debloat Toolbox I disabled as many apps/services as possible or useless to me.
And to block the last bit of amazon shit I use my router (fritzbox) to do some extra domain-blocking for the following domains:
mads.amazon-adsystem.com
images-na.ssl-images-amazon.com
ags-ext.amazon.com
arcus-uswest.amazon.com
cdws.eu-west-1.amazonaws.com
cognito-identity.us-east-1.amazonaws.com
cortana-gateway.amazon.com
cz15y20kg2.execute-api.us-east-1.amazonaws.com
dcape-na.amazon.com
device-messaging-na.amazon.com
device-metrics-us.amazon.com
device-metrics-us-2.amazon.com
digprjsurvey.amazon.eu
dp-discovery-na-ext.amazon.com
dp-gw-na.amazon.com
dp-rsm-prod.amazon.com
messaging-director-us-east-1.amazon.com
msh.amazon.co.uk
msh.amazon.com
prod.amazoncrl.com
tap-client-stats.s3-eu-west-1.amazonaws.com
todo-ta-g7g.amazon.com!<
Thats my way of using a cheap FireTV stick with no or at least minimal connections to any ad- and or tracking-servers.