|If you have flac files that are zipped--in the case that zipping makes a file smaller for easier download or several files are zipped to make them a single download--then it's a two-step process to convert them to mp3's. You have to unzip them to get the actual flac files and then you use a conversion program to convert them to mp3's.|
But you're describing it as if it's a single step--you were directly converting the downloaded files but now you can't do it. You mention that the downloaded files have a different file extension--they were .z0 and now they're .Z. I'm not familiar with those extensions but I'm guessing your browser was automatically extracting the files previously but now they're coming with the different extension and your browser doesn't know what to do with them so it leaves them alone.
IF that's the case you need different software to extract the files. In Derek's link it was suggested to use winrar or 7-zip. You might also contact the source from which you're getting the downloads to find out what they used.