As of Splunk 4.3 you are able to do this.
http://docs.splunk.com/Documentation/Splunk/latest/ReleaseNotes/MeetSplunk#Non-Flash_UI
And just to augment that answer , if you ever wanted to develop your own custom non-flash frontend rather than using SplunkWeb , then take a look at the Javascript SDK , http://dev.splunk.com/view/javascript-sdk/SP-CAAAECM , where you could use non-flash Splunk charts or perhaps 3rd party charts like Google charts and D3/Rickshaw.