The defender was the subject of three rejected bids by the Blues throughout the summer as the Robins kept their man.
Interest also arrived from Leeds United, but Flint was kept by Bristol coach Lee Johnson and the 28-year-old marked his stay with the club by scoring the winner in a 1-0 win over Reading on Saturday.
"It's been a stressful few months with everything being up in the air," Flint told the Birmingham Mail.
"There has been a lot of interest, which is flattering. But I've just got my head down and worked hard.
"Some other people might have chosen not to speak with me, but the gaffer has been great throughout, keeping me informed of what was going on."
Bristol travel to Molineux on Tuesday night to face Wolverhampton Wanderers before hosting Derby County.