I recently spotted a "crossed circle" system notification icon on my Fire HD 10.
What does it mean?
It means that you have not turned on the "hands free" feature of the Alexa app. Instead of just speaking to Alexa, you will first have to long press the home button to make her listen to you.
Circle with slash means you tapped the volume button and then selected "None". It means you are in silent mode. In some devices it's also when there's no cellular network.
It means hands-free Alexa.
You can change that on and off at the notification bar.
When this sign (circle with line through)is on it means that Alexa does not work, go to settings and activate Alexa and it disappears. Note :- this is on a Kindle Fire Tablet.