Real linoleum flooring is made with 100% natural ingredients including linseed oil, cork, limestone, tree rosin and natural minerals and it is installed with solvent free adhesives. We bought some for our home from a company named Forbo.
Here are some samples of original 1920s-30s(?) linoleum flooring I found here. I searched the web for examples to show you and they were hard to come by. We have some old crumbly sheets on the floor of our barn, of all places. And I found this interesting bit of information here: "And where most vinyl patterns are printed into the surface, linoleum's colors go all the way through. As linoleum wears, different layers of color are gradually revealed." I like this. That last link also has some suggested books and articles on linoleum if you want to take a look.
Above is a video made by Etsy's Tara Young of a cottage renovated in a 1930s-40s style. The owner talks about a 1920s linoleum rug which is quite beautiful and in amazing shape.