Keep this in mind, though, there's no actual evidence that dinosaurs did make "milk" for their offspring. They aren't mammals (who have breasts and lactate real milk). The link, suggested by Paul Else, of the University of Wollongong, is through the dinosaurs' avian descendants.
The theory was published as a commentary in the February issue of the Journal Of Experimental Biology.
He suggests that duck-billed dinosaurs known as hadrosaurs would have been a good candidate for "milk" producers. These dinosaurs wouldn't have been able to break down plant foods until they grew teeth and acquired the right gut microbes, but they still grew relatively quickly. This could be because of a nutritional milk-like boost from their parents, Else suggests.
Brian Switek, of the National Geographic blog Laelaps doesn't put to much faith into the theory:
... his hypothesis is undermined by the relationships of birds that produce milk-like products.
All of the birds Else mentions in his study belong to a group called Neo aves, and each of the mentioned avian species produce the milk-like substance in different ways. Pigeons generate the fluid in their crop, for example, whereas emperor penguins secrete the liquid from the lining of their esophagus. This hints that the ability to produce such substances evolved multiple times within Neoaves, rather than being a shared feature that goes back to non-avian dinosaurs.
He also says that since alligators and crocodiles don't show this, it's unlikely that the trait comes from their shared ancestor with birds, Hadrosaurs and other dinosaurs — an early archosaur that lived about 249 million years ago.