The Falcons have not had many streaks in team history where they haven’t allowed a touchdown by an opposing team for more than a single full game. As a matter of fact, they’ve only managed that feat five times in their entire history, including two three game streaks a long, long time ago.
The last Falcons team to do it was the 2006 Falcons, who went 2-0 scoring 34 points and allowing just 9 over two games in September. They managed to do it in 1993 (over two games, they scored 33 and allowed 30 somehow, going 1-1), in 1977 (going, improbably, 2-1 over three games despite scoring 24 and only allowing 6), in 1973 (scoring 58 points and allowing just 3 over two games, going 2-0 in maybe the most impressive streak in team history, and in 1969-1970 (3-0, scoring 51 and allowing 9).