The KMC, which I guess is what you are using to upload the file, is written entirely in Flash [a HTML5 implementation using Angular is in the works but we can’t commit to an ETA yet].
However, if you managed to log into KMC and attempt an upload, I’d say your problem is not that your browser doesn’t support Flash:)
Please provide a more detailed description of the steps you’re following and what you see when you perform them.
In addition, open your browser’s dev tools and check for errors in the “Console” tab as well as failing requests in the “Network” tab. Once you have more information, I will be able to help you further.