I have always felt more comfortable doing flying changes on my warmbloods. They have a flexibility about them that makes that movement very easy for them provided they are properly aligned.
I always have had a little more trouble with the stockier horses getting them to change leads properly and cleanly. I have been taking several clinics this year and made a point to take a stocky mare that was ready to start her changes.
In preparation for changes I really showed the mare how to narrow the base of her shoulder so that she could carry herself better and swing through and have an uphill balance. Many stocky horses are quite base wide in the shoulder and this causes trouble in the flying change. It seemed like the best way to narrow the base of the shoulder was to do haunches in with my whip in the inside rein and use it at the shoulder is she became wide in front. If you are not sure if your horse is base wide in the shoulder, try increasing the bend a little within a haunches in or half pass. If this is hard, then the shoulders probably are a bit wide. Just work to get a little better bend and this will help.
The horse I was riding in the clinics liked to carry her haunches to the right all of the time a little bit. This caused problems in the flying change too. So the haunches needed to be aligned before a proper change could occur. It the trot I would do renvers into shoulder in to help solve this.
In the canter when the rider is ready to do the flying change, the rider must align the horse. When traveling right to left lead, the haunches had to be pushed to the left and the shoulder moved to the right and then ask for the change. This required me to keep close track of my canter alignment and have a better diagonal connection.
In the canter left to right I just had to ride a little shoulder in to the right to get the right hind under the horse and then the change could come through easily.
Figure out any lateral imbalance in your stocky horse and you will have better flying changes.
Good Luck and have a great ride every day!