[beckler]

I'm sure you could use Wireshark and see what requests are being made, however, they very likely use TLS so getting the content of those requests would be extremely difficult if not completely impossible.

However, if you don't mind potentially destroying your echo, I'm sure you could reverse engineer a way to see what's going on.

[detaro]

As far as I know, only this year's Echo models don't have a known way to root them, so you could likely circumvent the encryption on an older model to inspect traffic. I'm not aware of any publicized results of someone doing that though, and it doesn't necessarily tell you what the backend can and can't extract from the audio data.