Thornton, 25, was cut loose after a little over a year in Green Bay. He has three years remaining on his four-year, $2.22 million rookie contract that included a $563,252 signing bonus.
Thornton will make a base salary of $523,000 for the 2015 season.
He has yet to appear in an NFL game.
Fleming, 23, is in the second year of his four-year, $2,520,584 rookie contract that included a $300,584 signing bonus. He stands to make a base salary of $510,000 for the 2015 season.
Last year, Fleming appeared in seven games for the Patriots.