Currently, Prime Video Channels are only available to watch and stream from within your home country.
The selection of titles included in Channels subscriptions are not available while traveling outside of your home country. Due to geographical restrictions, while traveling internationally you won't see this content, or have the ability to sign-up to new Channel subscriptions.
If you have a compatible device, you are able to download titles before you travel in order to watch offline anywhere in the world.
Note: Residents of the European Union, while traveling within the European Union, are able to sign-up for and have access to the same range of Prime Video Channels and titles that are available when streaming from their country of residence.