The call centre are not the right people to get your flights credited and there are very few reports of people getting their accout credited this way.
The best thing to do is sign in to your Diamond Club account online.
Then click on the link on the left hand side
Then click on the link to claim for flights
Then follow the instructions on the screen and submit your claim along with proof of your boarding cards / ticketing.
It can (and usually does) take up to 28 days to be processed, but this the best way to get flights credited. If you are close to the end of your membership year, then they will apply the credit retrospectively so you won't miss out on Silver status.