You should update your flash version the the latest available, but I don't think this problem is related to your distribution, but settings that you are using.
Ok, so not working on every linux. "Still my question, is there any non-flash alternative for chevereto script?" I need my site to work for everyone ;] or give me just the name od this flash upload script, and I'll look there ;]
Their is no way of bypassing the flash uploader except with the API, I hope this answer your question.
But you know Hubertus, if you want chevereto to be upgraded in future version with more possibility and fixs, we need details of your current configuration, so Chevereto can be upgraded and ameliorated.
The current uploader handler is maded on uploadify. And that implies that you need to have the flash plugin in your browser. You can check in the Adobe site that there are different Linux alternatives for this.
Pure non-flash uploader is in mind but uploadify should work on Linux as on any system that supports flash. Perhaps you are running an outdated web browser or you don't even have installed the plugin.
Uploadify need flash, therefore Chevereto needs flash.