Seashells themselves do not contain DNA. DNA is the genetic material found within the cells of living organisms, and seashells are the hard, outer coverings of marine creatures like snails and clams. These coverings are made of calcium carbonate, which is a mineral, not a living tissue.
While seashells don't have DNA, the creatures that created them do! The snails and clams that built the shells have their own unique DNA, and this DNA is present within their bodies, not their shells.
Think of it this way: A house is built from bricks and mortar, but it doesn't contain the DNA of the builders. Similarly, a seashell is built from calcium carbonate, but it doesn't contain the DNA of the creature that created it.