From the FAQs section of the website:
Is it legal for civilians to buy Body Armor?
In general, yes – for law-abiding folks. A felony conviction makes possession of Body Armor illegal under federal law and in many states. We have had civilian clients with many different civilian needs for Body Armor so we understand the need for vests for civilians. Our policy is to only sell to law-abiding adults who have a lawful purpose for Body Armor (A parent or guardian may buy for a minor with a legitimate need). Residents of Connecticut are prohibited from buying Body Armor unless the sale is face to face (or unless the buyer is a police officer, Police Department, or military).