How it was handled? He wouldn't speak with the team and conduct asking for a trade like an adult.
You seem to have taken the Flyers version of the story as complete fact. This is one of those situations where there is a significant amount of nuance that you're completely ignoring. They seemed to think that firing their GM was a "get out of jail free card" with regard to commitments that their previous GM had made. Nothing that Briere did was illegal, but I think that much more the definition of unethical and the level of hubris exhibited when the Flyers were surprised when the other party they screwed decided he no longer wanted to play there after that.
I'm someone at least considers a team's position when there are these "player vs. organization" conflict, and think I'm relatively fair. As was his right, Briere decided not to live up to what his predecessor committed the organization to. Part of that right was living with the ramifications, and when a team screws a very rare talent, it shouldn't be surprising that they are going to exercise their rights, which include not signing a contract with the organization. Top 5 picks typically aren't generic "assets" that can be easily replaced, and if you treat them poorly it typically will not end well for the organization.
Obviously - I don't have access to 100% of the actual facts and circumstances of this case. I did find it interesting, and read as much about the situation as I could. To me, it seemed like the Flyers were acting like the Red Sox whose standard practice is to weaponize the media and absolutely NUKE people who leave the organization. There is a really wide range of what could actually have happened. My intrepretation of what likely went down is Fletcher made promises to CG's camp that Briere didn't feel he had to honor, and Briere felt that he would be able to repair the relationship in the future when it came time to sign the guy he just screwed. When that was not possible, the Flyers controlled the narrative and took the flame-thrower to CG in the media. I think it's MUCH more likely that the Flyers screwed CG and soured the relationship, rather than CG just went borderline insane one day for no reason. YMMV.
EDIT:
Philadelphia Flyers put F Ryan Johansen on unconditional waivers, citing material breach | TSN said:
"He's going through some kind of rehab," Briere told NHL.com June. "He had an injection; claims he has a hip injury. At this point, honestly I'm not too sure where it's at. We're not sure if he's going to need surgery, or if he's going to be ready for camp. We don't really know at this point."
This is what I mean by smear campaign (note this is from June). Briere makes multiple statements "claims he has a hip injury", "I'm not too sure where it's at" that make you believe that the Flyers doctors have not been involved in this situation at all, and is 100% insinuating that RJ is a malingering POS. Based on his reputation, maybe RJ is that, but calling him out in the press when you're the GM isn't necessarily the best way to go when you potentially need to negotiate with him going forward. Likewise - screwing the most important prospect in your system by offering him an AHL try-out instead of signing him and burning a year off his ELC as promised (and is common practice for other highly thought of prospects across the NHL) likely is not be the best way to start off your hopeful long-term relationship with a foundational piece of your organization. I would have hoped that any of the ex-players (Briere, Jones, Lindros) would have enough self awareness to see how those actions might decrease the likelihood of a good relationship moving forward. But it seems like the leadership team immediately relied on "This is best for the Flyers, and if you don't acquiesce we're going to brand you as a selfish POS.". A bit ironic when you think about Lindros' history regarding the Flyers training staff. Organization leadership wants to use "this is a business" to justify every action they make, but then are shocked when players don't sign up to take one for the team because it's also a business for the player. I'm generally "pro-team", but that is complete BS.