What evidence links birds to mammals in evolution?

No evidence links birds to mammals in evolution. However, there is evidence that birds evolved from dinosaurs. In fact, some biologists call birds "living dinosaurs".

Birds have a similar hip structure to one class of dinosaurs, the ornithischians, but are actually more closely related to "lizard-hipped" or Saurischian dinosaurs, an order which includes the theropods such as Tyrannosaurus rex. It is now known from fossil evidence that some theropods had feathers, not only for warmth but also for display. They would have looked remarkably like birds, apart from the inability to fly.

The lines that led to mammals and dinosaurs separated about 325 million years ago with actual mammals and dinosaurs appearing at roughly the same time about 235 million years ago. The first birds evolved from dinosaurs about 220 million years ago.