How to keep mutalisks moving?

Solution 1:

As it said in liqupedia

Like all units without firing animations, Mutalisks can attack while remaining at full movement speed, if issued the attack command followed instantly by the move command.

So, press A-left click-right click at ground (not unit). If attack cooldown is not elapsed then mutalisks will continue to move futher. Otherwise they attack and continue to move at full speed.

Solution 2:

What their slow acceleration refers to is the time it takes them to reach top speed. When stopping to fight, there is no way to keep them at top speed. They will stop, shoot and when you issue another move command they will slowly build to top speed. You can abuse this a little by micro. As long as you don't let your mutalisks reach a full stop it should cut down on their acceleration, this can be accomplished like a 'scoot and shoot' marine micro with attack followed by move commands.

This concept however is bigger in muta placement then muta micro, here is an example when you should be aware of this:

You have a flock of mutalisks that you intend to attack the mineral line with. You can sit just out of LOS while you prepare your attack and then attempt to fly in to hit the mineral line. But because they take a long time to accelerate, your opponent will have a better chance of reacting and defending your attack.

However, if instead of staying just out of LOS you keep your mutalisks even farther away, your mutalisks will have a 'running start' and enter your opponents base at full speed.

Solution 3:

One method is to patrol-move the Mutalisks in a circle, for example. This will keep the Mutas at their maximum speed. However, the Mutas will still stop and attack if an enemy comes into range. But with quick enough reflexes it should be possible to command at least some of the Mutas to move away without losing any speed.