Flores's return following the dismissal of Javi Gracia after four games of the Premier League season seemed to be going flat as Pierre-Emerick Aubameyang struck twice in the first half.
But Tom Cleverley halved the deficit in the 53rd minute after some dreadful Arsenal carelessness and Watford were rewarded for a much-improved display when substitute Roberto Pereyra converted an 81st-minute penalty awarded after he was brought down by David Luiz.
Watford came agonisingly close to winning it with Gerard Deulofeu curling just wide and then Abdoulaye Doucoure having stoppage-time shot saved by Bernd Leno after a counter-attack.
Victory would have put Arsenal into third place but they ended the day seventh in a cluster of clubs on eight points.
Watford are still seeking a first win of the season and remain bottom but they doubled their points tally to two.