QuarkXPress 10 does not offer the ability to export to Flash anymore.

Though it was innovative and award-winning functionality to allow authoring Flash (SWF) with QuarkXPress 7, 8 and 9 – enabling designers to create interactive experiences without having to code - the trend has moved on. The hay days of Flash are long over, it's all about HTML5 now.

QuarkXPress 9.5.x is the last version to support Flash (SWF) export and the Interactive layout.

Important note: As QuarkXPress 10 will not open projects that contain any Interactive layout, you need to convert these layouts to a Print layout using QuarkXPress 7, 8 or 9, and then open these projects in QuarkXPress 10.

For more information please refer the link: http://forums.quark.com/t/33059.aspx