If they hashed the user input, it wouldn't matter what the client gave them in terms of password requirements. Spaces, special characters, arbitrary lengths up to tens of thousands of characters would all be fine with a cryptographic hash, there's no way the resulting hash would be anything but a fixed length of n bytes. Nothing "evil" can make it through being hashed.
The password requirements Flickr has set show that they are not using a cryptographic hash, the limitations on length and character set imply that they are being stored incorrectly, either in plain text or a space delimited format. There's no reason to have these limitations if this were not the case.