The 22-year-old King signed as a rookie free agent out of Auburn in May. He released Sept. 5 and signed to the practice squad Sept. 7.
The 29-year-old Fletcher signed as an unrestricted free agent from Philadelphia in March. He played in two of the Patriots' first three games, making 10 tackles and forcing a fumble. He has played 73 games, making 54 starts, in seven seasons with St. Louis, Philadelphia and New England.
New England is at Dallas on Sunday.