Score along the top edge of the cove base where it joins to the wall with an utility knife to break the paint or other finish seal between the cove base and the wall. Be careful not to cut into the wall and apply gentle pressure to the knife so that you are just cutting through the finish.
Position the flat blade end of the trim molding flat bar on the top, back edge of one end of the cove base. Tap the opposite end of the bar with a mallet to ease the blade of the bar between the wall and cove base.
Pull the bar toward you in a gentle motion to slowly separate the cove base from the wall. Work your way along the entire length of each segment of cove base in the room in this manner.
Apply more pressure to the bar as you pull the bar toward you along each length of cove base to completely remove it from the walls. Carefully lift the cove base from the wall and remove it from your kitchen space to avoid damaging your flooring.
Inspect the floors and walls where you removed the cove base and pull out any nails that might have been left behind, using a nail puller. Be careful not to dent the flooring or wall as you pull out the nails. Place a block of wood under the end of the nail puller as you pivot it toward you to pull each nail out.