There is no record for a "perfect season" in regards to field goal kicks.
National Football League
Field goal range
Goal refers to a method of scoring in many sports. It can also refer to the physical structure or area of the playing surface where scoring occurs.
In several sports, a goal is the sole method of scoring, and thus the final score is expressed in the total number of goals scored by each team. In other sports, a goal may be one of several scoring methods, and thus may be worth a different set number of points than the others. A few of these sports use the term field goal to distinguish one scoring method from another.
Field goal range is the part of the field in American football where there is a good chance that a field goal attempt will be successful.
A field goal is normally 17 yards (7 yards in Canadian football) longer than the distance of the line of scrimmage to the goal line, as it includes the end zone (10 yards) and 7 yards in which the holder stands behind. In Canadian football, the goal posts are on the goal lines, in front of the end zones. Therefore, if the line of scrimmage is at the 30, the field goal would be 47 yards (in American football) or 37 yards (in Canadian football).
field goal kicker
Stephen Carroll Gostkowski (pronounced "gust-OW-ski") (born January 28, 1984) is an American football placekicker for the New England Patriots of the National Football League (NFL). He was drafted in the fourth round of the 2006 NFL Draft with the 118th pick, one of just two kickers drafted, and the only rookie kicker to make an NFL roster that year.
Gostkowski, who played both college football and baseball for the University of Memphis, is the most accurate kicker in Patriots history, and one of the most accurate kickers in NFL history. He is also a consistent and prolific scorer: he is only the second player in NFL history to score 500 points in his first four seasons in the league. Also, given the Patriots' propensity to find the end zone, Gostkowski holds the record for most extra points in one season, with 74 in 2007 (and the second highest total in NFL history, 66 in 2012).