@SlackHQ It's really a shame. It isn't possible to send a file via iPad app. There isn't any reaction if I tap on "Add a File" in the 'fancy' new file dialog. So Slack will become more and more unusable besides the missing screensharing features.
Hi Thorsten! The Add a File dialog should absolutely react when you click on it. It sounds like you're experiencing a bug we're looking into right now. 
We appreciate your patience while we work on a fix.