I have all the required firmwae / software updated for the intel graphics card 620 running on i7 Kabylake and still DxDiag under HDR support it gives me not supported (I have attached it along with Intel system support utility). As per my understanding Intel 620 should support HDR in Windows 10 however that option under display setting is not even visible.
I understand that you are not being able to turn on the HDR support with your system.
Regarding this, I would like to mention that we have an article that can be followed explaining what needs to be taken into consideration and the steps that need to be followed in order to be able to turn on HDR. Please refer to the link below:
Make sure that you have followed all of the steps mentioned in that article so that there is no problem with the HDR.
I hope this helps.
I am following up with your case and see that we have not heard back from you.
Were you able to check the article? Did it help?
If you need more assistance do not hesitate to reply.