Your Sky box and your Amazon Firestick are, obviously, connected to your TV. You can't connect either of those devices
directly to your home theatre system but you can connect your TV's sound output to it, achieving the desired result.
Exactly how you do that though will depend on what type of sound outputs are available on your TV set. If you've got red and white phono output sockets available, you can connect them directly (using a cheap lead, available from many 'discount' stores). Similarly, if you've got a standard 3.5mm headphone jack on your TV you can use that. (Poundland can sell you a lead).
See page 23 of the user manual:
https://docs.sony.com/release/DAVDZ120.pdf