You can also go into a sidekick from a front to roundhouse position finishing into a sidekick. (1.lift+tuck hold 2.rotate to target 3. launch usually this is preformed with your rear)
the other would be 1. lift+tuck already facing the target with your leading leg and launch.) These bring in enormous combinations for your future kicking options, practice them both, basically lead&rear.
To focus on your problem for fluidity, simply practice the form slowly over and over. make sure you have a GOOD form. also a good trick is to hold your kicks once launched.
a simple but effective drill for starters:
side kick, hold 2sec
side kick hold 3
side kick hold 4
side kick hold 5
change legs
this will build your power, and speed as well as height. When you hold the side kick make sure you suck your glutes\butt in . Keep your back straight. and make sure your toes are pointing downwards(heel should be up), and rear foot on the floor, try not to go on the balls(you can do this, but your supposed to have your full feet on the floor)).
do this and everytime you should slowly try to lift and hold your leg higher. You will notice very small progression, but you will be progressing properly, and have good form,flexibility,accuracy control and speed.
when you have good form, slowly incorperate speed with control in the drill.
side kick,1,2,3,4,5,6,7,8,9,10 hold 5 sec
be creative, switch it around. to your liking
this is a beautiful, powerful and useful kick, and very easy to chain ontop or before of another kick(roundhouse to sidekick without putting the attacking leg down is very simple) once mastered.
anyways I mentioned most things people said here, except I dont think anyone mentioned the butt, its very important. If people here havent done it, I highly recommend you give it a try, you will notice a power shifting difference.
I will correct any mistake on this post i might have made later tonight

no time to review
Here`s 2 other cheap\free method to get your kick higher.
1,If you have a partner, get a small bean bag or even a hacky sack, hold the position the highest you can, than have him slowly put it on your foot, hold it, your feet will notice the small weight. My aunt did that to me.
2. Practice your form at knee level(preform a side kick towards your knee level) as warm up, so you remind yourself how to end the kick.