I'm working on self-publishing a book on Amazon. I'm in South Africa, and don't have a bank account in the UK or US. I know Amazon will send a check. I'm curious if anyone knows anything about how this would be taxed - by America and S. Africa, or only by the local government?
Where you "are" is normally not decisive on where you pay tax, it is your country of residence (which might be South Africa or any other country) which determines where you pay tax. Having a bank-account in another country doesn't influence that, although where things get paid might have influence to the applicability of VAT, c.q. sales tax, or not. IIRC in the USA sales tax doesn't apply to sales outside of the states where the company (Amazon) has no offices, in the UK VAT rate for books is 0%.
If you have to pay income tax in your country of residence (there are only a few countries that not seem to tax you), you should probably declare that as income, as you would have to if you had bank accounts in the USA or UK.
The USA should not tax this (although they might ask for proof that you pay your income tax in your country of residence. I used to get special forms for that after moving from the USA to Germany).
Ask your tax advisor, to prevent double payment of tax.