The British No 1, who completely outplayed Flach to win 6-3, 6-4, 6-2, emulated the feat of Andrew Castle who was the last to achieve a third- round berth in 1987.
Henman remains on course to meet the American Todd Martin, who ended the Wimbledon dream of the 21-year-old in the quarter-finals this year. Martin had a less than convincing four sets win over Younes El Aynaoui in the first round.
On court 16, Flushing Meadow's third show court, Henman was always in control of the first set against Flach, a wild card entry and ranked 120 places below the Oxfordshire player at 159, as he swept through the opening set.
But Flach, who caused the sensation of Wimbledon by beating Andre Agassi in the first round, showed some of the fighting qualities which helped dispose of his compatriot early this year.
Trailing 3-1, Flach came back to lead 4-3, but Henman showed how much he has matured over the last year by keeping his nerve and composure to take the next three games and close out the set.
Then at 2-2 in the third, with both players having broken serve, Henman brushed aside the challenge of the American to sweep through the final four games.
Andre Agassi, the Olympic gold medallist finally reached the third round after early problems with Leander Paes, the bronze medallist in Atlanta. The sixth-seeded American was a set and two breaks down to 149th-ranked Indian before fighting back for a 3-6, 6-4, 6-1, 6-0 victory.
MaliVai Washington, the Wimbledon runner-up and 11th seed, rallied from two sets down but still lost to fellow American Alex O'Brien 6-3, 6-4, 5-7, 3-6 6-3. O'Brien, who unsuccessfully served for the match at 5-4 in the third set, recovered in the end to continue his recent success, which began by winning his first professional title two weeks ago in New Haven.
Jeff Tarango, whose Wimbledon tantrum two years ago brought him a fine and suspension, beat the 10th-seeded Marcelo Rios 6-4, 4-6, 7-6, 6-2 and then jiggled his body in a jeering salute to Rios' supporters. "I support their enthusiasm," Tarango said. "At the same time, they're cheering blatantly against me. After I won I figured I could give them a little razzle-dazzle."
Thomas Muster, the clay-court specialist, had no problems with the German Dirk Dier, winning 6-3, 6-2, 6-4. Muster's win sets up a third-round match of two former French Open champions. The Austrian now faces the Spaniard Sergi Bruguera, who won the French Open in 1993 and 1994. Muster succeeded him as champion in 1995.