If you are, first and foremost, sure that your reeds are properly adjusted, it's a matter of learning how to deliver what is needed by your combination of pipes/reeds. The bottom line is that you'll need to adjust your strike-in technique to meet the needs of your drone/reed combinations - so that they don't squeal.

Squealing is the drone reed vibrating at the wrong harmonic - usually two or four times the intended frequency.  Depending on the air flow characteristics of the pipes, your reeds may start vibrating at the wrong harmonic if the air pressure comes up too quickly or too slowly - or if it goes back down and back up again! 

Some drones squeal if struck in an a given way with some kinds of reeds.  I know that a very common brand of reed in a certain highly regarded brand of bass drone will commonly squeal upon a normal strike in, but a very gentle strike will do just fine.  Some reed/drone combinations "like" a strike-in right under the bass drone - or not! - or with a certain strength.  This sounds odd, but it's all true.  Experiment and you'll find the right way for YOUR pipes.

 

The most common cause of squealing is that piper who actually hits the bag, bounces off a little and then pushes again.  This causes the pressure to spike up, fall off and then come back up.  I see this most commonly amongst inexperienced pipers that are trying to strike in and get both hands to the chanter in two beats!

A controlled squeeze - faster or slower - from the right initial pressure - not too high or low - is what you want.  Once you start the pressure going up, keep it going up - never allow it to back off - and you'll do very well. 

Experiment by starting out without striking in at all, blow up your pipes by mouth bringing up the pressure slowly from a low initial point and see what happens.  From here you can add in a gentle strike.  Learn what your pipes need and learn to deliver it.