You would probably do the update within your CheckDatabase module, right after the SendEMail call:

                Call SendEMail(rngColumnStart.Offset(lngCurrRow - 1, 1 - rngColumnStart.Column))
                rngColumnStart.Offset(lngCurrRow - 1, 18 - rngColumnStart.Column).value = 1
18 being the column number of column R. It would be just as easy to do it within SendEMail:

rngstart.offset(0,18-rngstart.column).value = 1