If you need to download localization files at runtime and use them in a Flutter app, it's important to note that this can be a complex task that may require some coding to achieve. The implementation for something like this will depend on the localization library being used for localization. Some localization libraries use generated localization code, while others use bundled ARB or JSON files as assets to access the localization messages.
It's worth noting that downloading and using the newest translations in the app is something that already exists and is used in practice. This is known as Over-the-Air translations update, and some translation management platforms offer services like that. One of these platforms is Localizely.
Over-the-Air translations update is handy because there's no need to release a new version to the App Store or Google Play each time you need to fix a typo or optimize texts. Instead, you can simply update the translations on the platform, and they'll be downloaded and used by the app at runtime. With this feature, you can keep your app up-to-date with the latest translations without having to release a new version every time you make a change.