It's extremely variable, of course. Some proteins have half-lives of a few seconds, others can be in the millions of years.

Dinosaur proteins have been (debatably) discovered:

>Ancient proteins dating back 195 million years have been found inside a dinosaur bone. ... The discovery pushes back the oldest evidence for preserved proteins by 100 million years. ... "This discovery tells us that yes, you really can probably preserve soft, microscopic proteins inside dinosaur bones for tens or hundreds of millions of years," Dr Brusatte added.

--'Startling' dinosaur protein discovery

The record for identifiable, sequence-able DNA is around a couple million years:

>Here we report an ancient environmental DNA (eDNA) record describing the rich plant and animal assemblages of the Kap København Formation in North Greenland, dated to around two million years ago.

--A 2-million-year-old ecosystem in Greenland uncovered by environmental DNA

Of course these are not the normal circumstances. DNA in a rain forest would be completely gone in probably a year or less. Most proteins are far less stable than the collagen found in dinosaur fossils. But it gives you a sense of the upper limits.