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In Zilla, you can not switch between multiple Flickr accounts. But what you can actually do is disconnect/remove your account and then connect another account to upload to.
To remove a connected account follow the process below:
1. In the application window, click the little 'x' icon located in front of the connected Flickr account.
2. Once the account is removed, click on the 'Add Your Flickr Account' button to associate/connect another Flickr account and follow the authentication process as mentioned in 'How do I connect my Flickr account' help post.