Sending despatch emails to Amazon customer is against the Amazon Selling Policy. Therefore you need to ensure that No emails are sent when orders are processed.  There are several steps you need to follow:

1)       Go to Settings > Email Notification > Dispatch Notification Email

2)      Disable the “Default” Condition. If this is not done the Amazon emails will be sent regardless of the other conditions you have created.

3)      For each new condition that you add you need to add the following code:

Source <> ‘Amazon’ 

If you would like to expand this condition you can add an "AND"

You can then add the new condition (Source = ‘eBay’, cCountry<>'United Kingdom'  etc.) so that the email is only sent if the condition is met.

for Example Source <> 'Amazon' AND cCountry <> 'UK' this statement would stop anyone outside of the UK from receiving Despatch Notifications via email as well as Amazon sourced Orders

If you are using FBA you will need to ensure that with the Source <> 'Amazon' condition you add AND Source <>'Amazon FBA' it should read;

Source <> ‘Amazon’ AND Source <> 'Amazon FBA'

Please note that you only need to do this for the Dispatch Notification Email