THere's no law against law-abiding private citizens buying, owning, or wearing body armor. That goes for all its accessories, including the plates you're talking about.
Many states do prohibit its ownership by convicted felons, and/or have enhanced penalties for people committing crimes of violence while wearing it.
The trick is finding a place that will sell it to you. Most of the industry holds its products for police, military, and licensed security firms.
US Palm sells to the general public, I'm told; Google search will get you there.