Morten,
I have been writing TypeScirpt with Kendo references for more than one year, the compilation error happened only after jQuery.d.ts upgraded to 2.2.3 one month ago. Everything goes fine before 2.2.2.
It's easy to fix this issue by comment interface JQueryPromise<T> declaration in kendo.all.d.ts as a workaround, and I believe Telerik will fix it soon. Don't worry about using TypeScript with Kendo UI, just do it! Have fun.
Regards,
Jeffrey