secure document transmission for face image extraction

We know service supports over HTTPS and encrypted with TLS.

To clarify there, you cannot make API calls to Rekognition unless it's using HTTPS.

Is this client to server channel safe from any external intrusion??

For your best protection here, ensure you're using TLS 1.2 at a minimum.

Does this AWS rekognition provide any encrypted input data transmission support for e.g. client side encryption at rest ?

This is possible, but not something Recognition does natively. In order to do this, you would need to add additional logic to your application to handle encryption/decryption and your key material.

See the Rekognition security guide here..