I have experienced exactly the same issue. I chose to manually drill the hole with a 5mm drill bit but, as many if not all among K8200’s users, I now experience a “Z axis wobble” when printing parts due to a misalignment between the Z motor and its threaded rod.
So, if I had to do it again, I would perform the drilling on a lathe and hopefully reduce this undesired wobble from my prints.
Anyway, like I just mentioned above, this (cheap) shaft coupler usually ends up replaced by something like this one.
In this thread in page 14, look for a post from sv650s who did a good job describing a list of parts to successfully improve this K8200’s weakness…
the linked flex coupler at ebay is a 5 to 10 mm version, so it won’t fit the original M8 rod. But there are of course 5 to 8 mm flex couplers available in many RepRap online stores, so it shouldn’t be too much a problem to find one.
About the original coupler: if the motor shaft does not block immediately, but after a few mm, there’s most likely a small aluminium chip from the grub screw bore. A small file can be used to remove it.
In case a drill is necessary, make sure you start with 5.0 mm, not larger. The motor shaft is very precise, so if the drill fits, the shaft will fit as well. Drill very slowly, maybe even by turning the drill chuck by hand. This will reduce the chance that the hole becomes elliptical.