XamRibbonWindow apparantly has problems when setting FlowDirection to RightToLeft. The application icon will move over the Close / Minimize buttons of the window and texts are Mirrored! It is expected that application Icon / Menu appear on the Right (instead of Left) and texts appear normally, not mirrored. Things work fine when using a normal Window instead. Please see the picture.
This issue has been reported and should be addressed in a future hotfix. You should submit the issue to the support group so that you may be notified when the fix is available. When you contact the support group please reference issue #6238.