If you've got an uneven old kitchen floor of, say, lumpy ceramic, and you're wondering how you can cover it without ripping it up, consider a no-glue "floating'' floor. These floors come in kits of preformed planks that fit together at the sides to form a flat surface, but aren't nailed or glued to anything. Some new systems brag that they don't even need the usual layer of foam underlayment, but since you're covering an uneven floor, you'll want a kit that includes that cushion of underlayment.
Use your hammer and flat-bar to remove the floor trim from the perimeter of the kitchen. Keep it intact as you remove it, and set it aside.
Cover the whole floor in foam underlayment, rolling it out in courses and taping them to each other along their edges. Don't staple or otherwise attach the underlayment to the floor below it.
Lay the first course of floating floorboards along your starting wall, with the grooved edges of the boards facing the wall. Set shims between the boards and the wall to create a thin gap of about 1/4 inch there, to allow for floor movement. Attach the boards end-to-end all along the wall, cutting the last board on your mitre saw to fit against the perpendicular wall.
Set the next rows in place alongside the first row, attaching the boards by their sides and laying them in staggered courses (so the ends don't line up). Cut the boards as needed at the ends. Use a jigsaw to cut around the cabinets and any other obstructions. Cover the whole floor.
Nail your floor trim back in place, using trim nails and your hammer. Nail through the walls, not the floor. The trim should cover up the spaces that you left by the walls, while holding down the flooring.