In general, to hit a fast, flat serve your weight needs to be moving in through the ball which, as a natural result, brings you forward into the court, as well.
So, if you are not doing that, then you have a hitch of some sort in your serve. Why is your spin serve fluid, and your flat serve not? Since we can't see you from here, try to be self-observant and pay attention to what is going on as you serve (not during a game, obviously, but during practice, with a bucket of balls).
And, yes, what you need to do is practice. Slow down the flat serve a bit and try to get the feel of your weight stepping into the court or "falling" into the court as you strike the ball.
Then again, the problem may not actually be what you think it is. The spin/kick serves are slower-- for several reasons-- you hit it a bit less hard, it has spin/frictionwhich slows it down, and it travels in a longer arc which takes more time. All of that gives you more time to scoot your body into the court and get your bearings before the ball comes back.
So, it might be that your spin serves are not more fluid-- you just have more time to get set up-- anyway, that a possibility.
Normally, there are some pretty good players that hang out on the courts. You can ask one (maybe even your opponent) to watch your flat serve and tell you what they see. Or you can post a clip here if you are set up for that.