Hello,
I am having the same issues as in this thread:
It works fine in VST mode. Kontakt 5 and 6 work fine in standalone or VST.
I tried the fixes under this page: https://support.native-instruments.com/hc/en-us/articles/115004169849-KONTAKT-Crashes
None of those helped.
With the help of Sysinternals Process Monitor, I have resolved my issue. Jack (a toolkit for audio routing in Windows) causes Kontakt 7 standalone to crash for some reason (but not Kontakt 5 or 6). After uninstalling it, Kontakt 7 starts up just fine.