''No man is an Iland,'' John Donne wrote. Not even Dean Kamen, sole owner and resident of this rocky three-acre freckle in Long Island Sound, three miles off Noank, Conn. ''I am an empire!'' he boasts. Mr. Kamen, a 36-year-old bachelor and millionaire inventor who prefers to be called Lord Dumpling, has fulfilled one of life's larger fantasies. For $2.5 million, he has bought an island - complete with mansion, lighthouse and a copy of Stonehenge - and seceded from the world around him, or so he likes to believe.

Although owning an island in the Sound and considering it to be a land apart is not an unheard-of notion, few people have gone to such theatrical lengths to establish a semblance of sovereignty. Mr. Kamen's island has a Constitution, a Cabinet and a flag, plus currency, 1,000 dumplings to the dollar; a Navy, a surplus amphibious vehicle, and an Air Force, a helicopter. It also has a national anthem, with lyrics written by a Broadway director, Paul Lazarus, Minister of Brunch. The first verse, sung to the tune of ''America, the Beautiful,'' goes: O isolate With star-filled skies And crashing waves of foam From Moonwatch Hill to Great Stonehenge O blessed second home.

The birth of North Dumpling Island as an independent nation, which was spurred by a spat with New York officials last winter, may seem silly, especially when the bearded and blue-jeaned Lord Dumpling dons his coronet and comments on matters of state by saying, ''It's sooooo neat!''

His lordship, though, is no Zonker Harris, the royalty-loving man-child of ''Doonesbury.'' And his tulip-ringed island is neither a sandbox for old hippies, an opulent Fitzgeraldian paradise, nor a galling example of how kids can fritter away their trust funds. Rather, it is a talented workaholic's magnificent symbol of escape and reward, of achieving the ultimate home away from home, of going beyond - way beyond - the American Dream. Mr. Kamen, a native of Rockville Centre, L.I., who spends most of the year in New Hampshire, made his fortune creating and selling specialized medical equipment. He has also purchased a helicopter manufacturer.