Flores was soon given his marching orders by referee Phil Dowd for two bookings in as many minutes for challenges on Willian and Andre Schurrle respectively.
Despite their numerical disadvantage, Garry Monk's men proved a stubborn opposition as the West Londoners' tried in vain to capitalise on their advantage.
Samuel Eto'o could, and perhaps should, have broken the deadlock shortly before the hour mark after firing a half-volley wide of the post from inside the box.
Minutes later, Wayne Routledge galloped through the heart of the Blues' defence before thrashing narrowly wide the mark from a good position.
However, City's resistance waned and Ba broke it on 68 minute by running at defender Ashley Williams before burying his effort beneath the body of goalkeeper Michel Vorm.
Salah and Eto'o both had chances to put the game beyond doubt in the closing ten minutes, but the misses were rendered academic by the sound of the final whistle soon after as Jose Mourinho's side keep the pressure on the Reds.