Unless you are a QPC player, that’s literally impossible. Because flex implies in you being able to swap roles within the same match, to adjust on the very specific situation happening in the match. You might still be queuing for all three roles, and maintaining a similar SR across them, but that is not the same as being flex.
Now, you might have a different definition of flex player. If so, keep calling yourself a flex player, and let’s simply agree to disagree. Just be aware that when I talk about flex player, I mean those that are not shy from swapping cross-role if they judge the swap was needed to win the fight.
Different experiences, then. Maybe because I was the one jumping constantly from Rein to Torb to Brigitte to Symmetra (2.0) and always trying to neutralize the best player in the enemy team. That was my challenge in the game.
I wasn’t flexing because my team “needed a new tank”, I swapped into Rein because we needed a strong presence on the point, and he is the best character to contest close quarters.
I wasn’t jumping into Pharah because I wanted to carry my team to victory. It was because the enemy team had a lot of close range characters, and I knew no one would contest me in the air.
I didn’t played Moira to pretend to be a healer while still playing as a subpar DPS. It was because my team was full of close range characters, and thus, they would probably walk grouped most of the time, so it was easier to heal them with Moira than Mercy or Ana.
I had at the time of season 17, 9 heroes in my hero pool that I had full confidence I was able to carry my weight with them, and about other half dozen that I could play in very specific situations. That was my toolbox of flex, and having to constantly decide which tool I should use to win the next fight was thrilling!
You sound like you have a similar approach to the game, given how you say that you couldn’t specialize for long before going back to flex (presumably because it was more fun). But you also have one thing I didn’t.
You cared about your SR. Which is not right or wrong, just a different way to approach the game.
I stopped caring about my SR after season 3, when it was clear that I didn’t had the time, skills, or desire to perfect my gameplay to attain GM or Top 500 (the only tier with a unique reward). So, while I still focus on winning as much as possible, I don’t really care if my SR was going up or down. All I focused was in finding the characters I enjoy playing the most, and just getting better by raw experience.
Flexing is the reward on itself. 
Never seen so much trash play and staggering and lack of coordination… since Bronze.