SiteKiosk uses the browser engine of the installed Internet Explorer to render web pages. To minimize security risks you should therefore keep the Internet Explorer updated by using the automatic Windows Update feature that comes with the operating system.
Unfortunately there is the risk of so called zero day attacks. There was one just recently that affected the Internet Explorer and was covered extensively in the media. Because SiteKiosk uses the Internet Explorer engine it is also affected. While the security features of SiteKiosk do limit the attack options to a certain degree a possible risk remains.
It is also notable that one aspect of zero day attacks is, that even antivirus software does not help as a required signature update takes its time to become available.
This is where Microsoft EMET or Enhanced Mitigation Experience Toolkit comes in. The toolkit can be used to harden an application so that flaws cannot be used as easily and zero day attacks have no or a more limited effect. It is free to use and easy to configure.
When you install EMET make sure to select to install it for all users. After the installation is finished you can just add the SiteKiosk.exe and other applications you want to protect using EMET in the EMET configuration. That's it. You can keep on using SiteKiosk as you did berfore, but now with the extra protection that EMET provides.