Swansea have confirmed police were called to the club's training ground on Friday when the two centre-halves were involved in a heated exchange as they prepared for Sunday's 3-1 defeat to Tottenham, which extended the Welsh club's winless run to eight games.
Reports suggested Flores had brandished a brick during the incident, but this was denied outright by the club who said "no threats or altercations" took place between the two.
And the 26-year-old Spaniard has taken to Twitter to give his version of events.
In a series of tweets, he said: "I would like to clarify what has been said in the papers today and to be honest it was just an argument between team mates as it can happen sometimes in a training session or in any changing of any football team nothing more.
"I did not threaten anybody in any moment and even less with a brick. I consider myself a respectful person and a good team mate who likes the unity, closeness and create a good atmosphere around my team mates, if you don't believe me then ask my own team mates and coaching staff.
"To finish I would like to say that my relationship with Garry Monk has always been fantastic and still is, to a point that we spend the afternoon together yesterday.
"Any person that is involved in the business of football knows that these small arguments regularly happen in training sessions and even more when things are a bit more tense than normal for not getting good results.
"So I just want all you fans to know that Garry and I are two very committed players for Swansea city and it was not more than just a silly argument and nowadays things get blown out of proportion in the press and social networking.
"It's a moment to be united and focused on the FA Cup Saturday versus Birmingham and Fulham the following Tuesday in the League. Come on Swansea."
Former captain Monk has not played since September after suffering a knee injury, while Flores, who joined from Genoa in the summer of 2012, has struggled for his best form in recent months.
Monk also looked to move on from the incident, he told the club's official website: "I have been playing in the professional game for 20 years and training rows are nothing new in a competitive and pressurised environment.
"Recent media reports have blown everything out of proportion. Yes, we had words, but at no time was I threatened with a brick by anyone.
"Chico is a team-mate and we stick together for the betterment of Swansea City and the fans. That it is the case throughout the squad.
"The matter has been resolved and we all remain united, whatever nationality we may be, because we wear the same club colours and that is the most important thing.
"We are a tight-knit group; we always have been and always will be."