During the 1884 season, he led the Union Association (UA) with 12 triples, ranked third in the league with a .457 slugging percentage, and compiled a 23–15 record and 2.46 ERA as pitcher, and threw a no-hitter.

The newspaper reported that the team's new pitcher, Burns, was 5 feet, 7 inches tall, weighed only 140 pounds (a weight that, "with proper training, will doubtless increase"), showed good command of the ball and was developing an "up-shoot" pitch that was "a beauty.

"[5] A veteran player who observed Burns in spring practice praised his "clever change of pace" and shared the Free Press's view that "his up-shoots will be hard to hit.

He made errors himself, muffing a fly, and giving three men bases on called balls, but these were to be expected under the circumstances, and he has no cause to be disheartened; quite the contrary.

[1] In 1884, Burns joined the Cincinnati Outlaw Reds of the newly-formed and short-lived Union Association (UA).

He led the UA with 12 triples and ranked among the league leaders with a .457 slugging percentage (3rd), a .306 batting average (7th), 84 runs scored (7th), and 33 extra base hits (8th).

James noted that Burns did not make the grade with Detroit in 1883, became "one of the best players" in the UA, earning him "another look" in the National League, lasting only 14 games.

A newspaper account of his first game for St. Louis, on July 6, 1885, noted: "Dick Burns made his inaugural appearance as a member of the St. Louis Club, and distinguished himself in the sixth inning by making a remarkable running backward catch of a line hit from Gilligan's bat, which really saved the game.

"[26] Again facing tougher competition in the National League, Burns's batting average dropped 84 points from the prior season to .222.

[1] He appeared in his final major league game on July 23, 1885,[1] a 15–3 loss to the New York Giants in which Burns played center field, had no hits in four at bats, and committed two errors in three chances for the Maroons.

[27] In early July 1885, The Sporting Life reported that Burns was signed to play for the minor league baseball club in Waterbury, Connecticut, at a salary of $200 a month.

[1][29] In early June 1886, Burns, at age 22, was also given managerial responsibility for the club in Murnane's absence, becoming a player-manager.

[30] Burns concluded the 1886 season playing in the outfield, principally right field, for the Brockton, Massachusetts club in the New England League.

[12] In late July 1887, the Lowell Magicians of the New England League purchased Burns's release from the New Haven club.

[12] The Sporting Life reported that, while playing for Scranton in 1888, Burns had been "certainly one of the finest fielders, batters and base-runners of the Central League.

"[35] In late April 1889, The Sporting Life reported that Burns had not been signed for the 1889 season and was at his home in Holyoke, Massachusetts.

[40] In 1900, he remained in Holyoke, residing with his mother (Bridget Burns) and sister (Margaret Parker); he was employed at that time as a cigar dealer.