In short, it’s sparring but allowing each other to ‘flow’ from potential submission through to escape. I think the key part is to keep moving. Spend no time recovering in full mount, closed guard or back control, for example. Constant movement is the key to flow-rolling.
I like to treat flow-rolling like a musician would treat scales. A performing musician needs to warm up and more than likely they do this by playing scales. These movements are engrained in muscle memory and a musician can flow through them warming up the hands and switching the brain to ‘music mode’.
For BJJ, flow rolling is a chance to run through your scales on another body. The weight of you partner and their limbs are needed to ensure correct form and you need a partner to volunteer positions such that you can both roll between them.
Search youtube and you’ll find countless videos on flow-rolling. Most show two practitioners that obviously know each other well and can reinforce the links between positions as they move. Some videos even show the moves without a partner that loop around so you always return to the first position and can start again.
It’s a good idea to try out the new moves in the video otherwise you end up repeating the same movements and you run the risk of becoming close to a one-trick pony. To avoid stagnation, keep rotating ideas and adding new moves to keep flow rolling interesting.