I completed the California apportionment schedule in a partnership return, but nothing flows to column E of the CA 565K1 or 568K1.
You may need to check the box on the CA K1 screen Print Column E California source amounts.
The Help screen for this option explains:
Default all amounts in Column E to Column D (Direct Entry)
Check this field to default all the amounts in column E, to be the
amounts corresponding in column D. If nothing is entered in this
field and nothing is entered in the overrides for column E, then
the amounts in column E will all default to zero unless the
partnership is a full year California resident.
In your return, the partnership is not a CA resident.