Amazon manages each locale store's affiliate program under their respective store management and hence if you want to send traffic to another of Amazon's domains and get paid for it, you need to register for each program in turn.
Here is a convenient list to each of their home pages so you can sign up:
- Amazon United States (US) Associates Program
- Amazon United Kingdom (UK) Associates Program
- Amazon Australia (AU) Associates Program
- Amazon Germany (DE) PartnerNet
- Amazon France (FR) Club Partenaires
- Amazon Japan (JP) Associates Program
- Amazon Canada (CA) Associates Program
- Amazon China (CN) Associates Program
- Amazon Italy (IT) Programma Affiliazione
- Amazon Spain (ES) Afiliados
- Amazon India (IN) Associates Program
- Amazon Brazil (BR) Associados