Can you lay laminate or wood flooring over exiting linoleum floor?

Crystal, your two concerns will be, moisture and flatness. If the linoleum is flat, with no bumps or protruding tears, ( sand it flat if needed with an orbital sander) then it will act as an additional covering for the concrete slab, however you must use the appropriate laminate underlay. The underlay will provide cushioning and to some extent, moisture barrier. Do not lay laminate floor or engineered laminate wood floor, directly on the slab as moisture will be wicked from the concrete ( which is porous) and black mold and damage to the flooring will result.

The recommended procedure is to lay a subfloor first on the slab or linoleum. This can be achieved quickly and economically by using plastic backed, tongue and groove 2 foot, OBS squares, such as a product called ‘Dricore’. The plastic backing is ridged to allow air to pass under the sub floor, thereby keeping it dry and mold free.

With 2ft interconnected squares, the floor is covered quickly and a flat, dry surface is achieved upon which to lay the underlay and laminate.

This will provide a dry, warm floor.

Dear Crystal, remove the linoleum, it's going to crack eventually, then your floor won't be level. Put floor installation down on top of the slab.