When was the last drop kick used and is it still legal to use it?

Ray McLean of the Chicago Bears was the last player to successfully drop kick in the NFL. He converted an extra point following Ken Kavanaugh's 42-yard fumble recovery for a touchdown during the Bears' 37-9 win over the New York Giants in the 1941 NFL Championship Game. The drop kick came in the fourth quarter of the title game played on December 21, 1941. Hall of Famer Earl "Dutch" Clark is believed to be the last player to successfully dropkick a field goal in the NFL. According to game accounts, he dropkicked a 17-yard field goal in the Detroit Lions 16-7 victory over the Chicago Cardinals on September 19, 1937.

On January 1, 2006, Doug Flutie of the New England Patriots converted a point after touchdown by dropkick in a game against the Miami Dolphins. Flutie's dropkick for points was the first since McLean's for the Bears described in the above answer.

And just to clarify, yes, the dropkick is still perfectly legal.