Yea, Stanley Clarke does that finger flicking thing and he plays really fast with that technique.
Here's a few suggestions:
If you're having trouble going 1-2-1-2 on just one string then your fingers aren't used to the alternating motion. Whenever you find yourself doing nothing (or even if you are doing something that doesnt require much mental focus) put your hand against a table or your leg or any surface and just alternate the two - 1-2-1-2 and keep doing it. When you're use to it, it should be easy to translate it to the strings.
If you're having trouble when moving across the strings then you could try the minor and major scale, but thats boring.
The spider exercise is a very good one for that, even though it's meant to help your fretting fingers.
In case you don't know it, it's really simple (sorry it's not a tab, but a tab can't tell you how to position your fingers):
Grab any fret on any string (for this example let's say fret 5 on the D string). Hold it with your index finger and pick with your index.
Next, pick the fifth of that note (in this case the 7th fret on the G string). Hold it with your ring figner and pick with your middle.
Then you move by one fret higher (6th fret on D). Hold it with your middle finger and pick with your index.
Now the fifth of that note (8th fret on the G). Hold it with your pinky and pick with your middle figner.
Move on to the next fret (7th fret on D). Hold it with your ring finger and pick with your index.
A little twist, you play the major third this time (5th fret on the G). Hold it with your index and pick with the middle finger.
Then the next note (8th fret on the D). Hold it with your pinky and pick with your index.
Finally, the major third again (6th fret on G). Hold it with your middle finger and pick with the middle finger.
You can play this anywhere you like. It is a good exercise because, in order to get fast at it, you MUST use both picking fingers and constantly alternate.
Also try learning Paranoid by Black Sabbath. If you want to be able to play that song at regular speed without getting tired, you have to alternate fingers (or flick one finger as rushfan stated).
If you want to get any type of movement down, don't cheat. Do it as slow as it needs to be and constant repetition.
When practicing slap I played things as slow as 40 beats per minute for a whole week in order to get the movement down. After that I only raised the speed up to 50 and stayed there another week and so on.
Training your body is a very tiring process, but in the end - all those movements become simple reflexes and you don't even have to think about it anymore.