Can I measure velocity from an accelerometer? How accurately?
The sensor in itself can't provide you the velocity. I have used it accelerometers in a couple of projects the easiest way to get the velocity is to constantly monitor acceleration changes and calculate velocity instantaneaously.

In order to do so follow these instruction. Pleas note that this is only 1 axis reading in actual case you will have to perform this for all three axis i.e. x,y and z.

I hope you are aware of the equation of motion (V = Vo + at)... The sensor will provide you value of acceleration at any given time. But acceleration can vary quite significantly during a huge time intervals so keep the time intervals 't' small. Lets say t = 10ms (depends on you). So calculate V after every 10ms intervale and this will give you current velocity at any given time. But what about Vo? As you know it is refered to as initial velocity so in the beginning it will be 0. Immediately after first reading when you are about to take second reading the Vo will change to the previous V calculated and hence forth.

This means Vo at any given interval is actually the V calculated in the previous interval.

I tried this method in my project when using accelerometer. hope it helps you as well.