"Go slowly and practice" are two pieces of advice that will make anyone smooth over time. However, they're also two of the most obnoxious answers - they're simply a means to be smooth without regard as to what makes a flourish smooth. Also, fluidity can be achieved much more rapidly than simply through repetition, but you have to know how to practice.
The true answer lies in muscle memory. All flourishes have easy parts and hard parts. When you learn a flourish, you usually learn all parts of it at once, and practice the flourish in its entirety over and over. However, the learning curve for the hundreds, even thousands, of intricate muscle movements required for each flourish, whether a sybil cut or a fan, is wildly different.
In other words, you're going to get very good at one minuscule muscle movement for a flourish very quickly, while another will take you much longer to learn. And since choppiness is a product of irregular pacing of a flourish, if you practice an entire flourish over and over it's going to be choppy - and remain choppy - until your muscles "top out" and perform all parts of the flourish at their maximum capability (not just speed, but also strength and stability).
To solve this problem and cut down the time it takes to become smooth, all you have to do is practice differently.
When you learn a flourish, pay very close attention to how your muscles respond to it. Which parts are easy? Which parts are hard? Once you know this, you can focus on the harder parts of the flourish, bringing them up to speed with the easy parts. This will make you smooth much more quickly.
So spend your time on the move that makes you drop the cards, on the part of the cut that your muscles can't seem to get right, and on the places where you always lose control and balance. Instead of repping whole flourishes, micro-rep very small parts of them. If you practice in this way, once you string the entire flourish together, you'll be smooth.
Of course, this type of practice is neither easy nor fun. We all want to practice what we're good at, and it seems counterintuitive to "waste your time" repeatedly dropping cards re-working the hard parts of a flourish when you could be making what you're already fast at faster. Yet if you dedicate a block of time to building muscle memory for what you're bad at without getting distracted or giving up, you'll become very smooth in a much shorter amount of time than you would if you took the advice of "go slow and just practice more."