For complex itineraries like this from LHR - KOA, I'd definitely consult the "Where we fly" map on the website (link: http://dl.fltmaps.com/en)

This will help show that out of KOA Delta flies to Seattle and LAX,but it looks like the Seattle flight is only on Saturday's with the LAX flight running Daily.

Unfortunately it looks like both the LAX and SEA flights are running with the lousy 757 configuration, no flat beds and 3 rows of C+ in the FC cabin. I checked American and United and it looks like they all are only flying the 757, 737 or 321 into KOA, no widebodies unless you want to connect in HNL.