I don't have the Amazon Music Unlimited service, but from what I've been able to read, the Windows app uses the WASAPI protocol in shared or exclusive mode, but is unable to change the sample rate dynamically, so the only alternative you have is to set manually the rate at which you will play through the K7 in the Windows sound controls for this device. In your case, I guess you are interested in the highest possible quality available on Amazon, which is 24bits and 192 KHz. At the end I attach a guide to properly configure the application, taken from another forum.I’m running it via the Amazon app on my laptop. The sound quality is good but I’m stumped why it’s not changing hz frequency.
Another step I advise you (if you have not done it) is to install the K7 driver supplied by Fiio, so that during playback you can click on its icon and check the sample rate that your device receives.
Amazon Music configuration guide for 24/192:
Right click windows speaker icon > Open sound settings > Select output device > Device properties > Additional device properties > Advanced > Set default format to 24 bit @ 192000 Hz.
Go back and select output device > some other device not the one you want to use with Amazon Music. Don't skip this step.
In Amazon Music desktop app:
Set Audio Quality to HD/Ultra HD
Set Loudness Normalisation to OFF
Set Allow Exlucisve Mode to ON
Play a HD(24 bit @ 192000 Hz) track
Cliick the speaker icon and select the output device and set the Exclusive mode slider to ON
Click on the [HD] icon beside the track controls. Notice how Quality, Capability and Playing are all 24 bit / 192000 Hz
I hope this helps.