The pair were involved in a training ground incident in which the Spanish defender allegedly picked up a brick during a heated row, leading to police being called to the club's training ground.
The two have subsequently settled their differences and Monk confirmed centre-back Flores is in his plans for Saturday evening's south Wales derby with Cardiff at the Liberty Stadium as he prepares to name his first side since taking over from sacked boss Michael Laudrup.
"Chico will be involved in the squad. We have absolutely zero problems," said Monk.
"To be fair, I was talking to him today about tactical stuff.
"Me and Chico have had a fantastic relationship, honestly, and everything that has gone on outside has been blown up and we have had a laugh about it.
"There are no problems whatsoever, Chico is a good man."
Monk admits he is delighted to be given the chance to manage a team he has been with for the last decade and is determined to stamp his authority on the position.
"I just have to concentrate on preparing the team and I have to do it the way I feel is best," he said.
"I've always said I would be prepared (to take over) for the club and that is all I have to be. I am not trying to follow or be someone else, all I can be is myself.
"I've been here for 10 years now and I know everything about the club. I know about the players and the reputation we have built up.
"I think the club felt that and felt that in this situation, I was probably the best person to take it on.
"My status at the club is well known and I have always thought about coaching and management.
"I have been doing my badges over the past couple of years and I have been taking the Academy kids. It's always something I have been gearing myself up to.
"As my ultimate aim it would be great to manage this club. It's one of the proudest things I could ever do and to get the opportunity as it is at the moment...I couldn't be prouder."
Monk also confirmed he is not planning to play while in charge at the club and will instead focus on leading the team.
Meanwhile, the website founded by former England manager Glenn Hoddle has denied he has expressed any interest in the club.
According to zapsportz.com, Hoddle "has neither sought nor applied for the Swansea post. And he has not been interviewed nor has he any plans to be interviewed for the job".
Hoddle is a regular pundit for Sky Sports but has been out of football management since he left Wolves in 2006, having previously worked at Swindon, Chelsea, Southampton and Tottenham.
Garry Monk will lead Swansea in the south Wales derby on Friday. Coverage begins on Sky Sports 1 HD at 5pm.