I shudder when I hear people say it... a new round is starting and two students go to slap hands when one of them says "Let's just flow roll", urgh.
Why is flow rolling bad? Well, it isn't all bad but it certainly isn't rolling. During the full sparring part of a class, that's what you should do, full resistance sparring. Jiu-jitsu is fighting, that means you try to tap your partner and stop them tapping you. Now, there are different intensities to rolling, it shouldn't be flat out all the time, you are trying to learn and improve... but it should always be realistic, so that means you both resist each other's movements. Don't waste rolling time by doing anything other than full resistance sparring. It's the whole reason why jiu-jitsu really works in a fight and what keeps it from becoming just another nonsense martial art.
So, does flow rolling have a use? Definitely yes, but like most things there are right and wrong ways to do it...
I've already said that it's not a replacement for full sparring. It should be seen as a type of drilling, a time to improve your technique, reactions and "feel" for movements. Except for maybe in an advanced class, it's unlikely time is gonna be set aside for this in a regular lesson, so if you're going to do it then it's probably best before or after a lesson.
It's also important to flow roll correctly, and it's something that most people can't do... at all. I don't think it's worth finishing submissions at all when flow rolling, but you definitely shouldn't be trying to tap or control each other (that's full resistance sparring again). You and your partner have to be able to engage in a natural ebb & flow of one person taking control for a bit then switching over. So at any point one person is the attacker and one person is defending. The person attacking shouldn't be controlling any position ultra tight and the person defending shouldn't be trying to shut them down but should offer up different movements/options to be attacked. Then at some point the attacker should back off, which signals to their partner that they should now take on the role of attacker.
Your aim in these flows should be to improve your transitional attacks and learn what options you have during them. However, you can't start doing unrealistic stuff or get loose and sloppy with technique. This means that, like good technique drilling, you both have to judge the level of control you are using well at all times. You can't be too tight so that it just turns into normal sparring but neither can you be too loose that things become unrealistic... basically you need to work in the same was as when drilling technique; you don't try to stop each other but you don't let each other do stuff which wouldn't work under full resistance. This balance of realism should also be maintained beyond just a technique perspective... so if you try to hit a rolling armbar as your partner turtles, and you fail miserably, you should switch to defending while your partner starts to attack.
Due to all this stuff, I think flow rolling is something that white belts will struggle to do properly. I'm not saying it's impossible for them but to flow correctly you need a good knowledge of techniques from all positions, good movement and no ego at all. Most white belts don't hit all those marks, neither will some coloured belts though!
Flow rolling has it's place, but see it as a type of drilling not sparring and hopefully it will be another training method you can use to improve your jiu-jitsu!