Are you thinking of replacing linoleum flooring? Why rush into making a decision when you can easily paint over it in the exact colors you want? After all, if it still needs replacing, you can easily proceed with it.
There is an opinion that paint (the usual floor paint) is more solid on the linoleum than over a wooden floor. Linoleum surface is usually smoother than wooden floor surface, that’s why linoleum looks more beautiful than its wooden colleague.
Before you start painting the floor, wash it and let it dry. If you have wax on your floor, use a wax remover first. You can prepare cleaning solution yourself. For that purpose mix ¾ of hot water and a glass of calcinated soda (linen soda). Wash the floor with a brush to remove wax. Otherwise, it will prevent the oil paint from drying. After that wash the floor with pure water and let it dry.
If you have the wax covering penetrated into linoleum pinholes, dry the floor with a sponge treated with turpentine or aviation petrol. Turpentine or aviation petrol will dissolve wax in the linoleum pinholes. Do not use the usual petrol for that purpose.
When linoleum is dry you can cover it with different types of polish: oil polish, resin varnish etc.
When polish dries paint the floor. If you do not have any polish, you can paint the floor without polish base. Just make sure that linoleum is absolutely clean. Any dirt will show through the paint and make your linoleum floor look lumpy.