The "thousand year" number was roughly how many years the Holy Roman Empire lasted. The Holy Roman Empire was considered by Hitler to be the First Reich, with the German Empire being the Second Reich. So Hitler wanted his Reich to last a Thousand Years so as to be as great as the First one. There was also a religious significance as a radical Christian denomination referred to as "Millennialism" says something roughly along the lines of "When Christ Returns, he will rule for a thousand years." Arthur Moeller van den Bruck in his book, Das Dritte Reich, argued that that German history could be divided into three periods:

First Reich

Second Reich

Third Reich

This book was influential among the Nazis and was where we get the whole "Reich" terminology from. Van den Bruck argued that the leader of the Third Reich (he was writing in the early 20s before the Third Reich) would be a "German Messiah." So there was religious connotations about Hitler being Germany's Messiah and thus reigning for a thousand years.