Um... bluebird?????? What the????
Better let every Dressage rider world wide know that they can't use half halts in any pace but walk then?
A half halt is used to rebalance a horse, and shift more weight to the hind legs. Generally in preperation for a chance of direction or pace. Depending on the horse, I can ride up to 20 half halts on a 20m circle, in walk, trot, canter (including in any lateral movement I so desire to ride at the time). Half halts are NOT simply almost halting to slow the horse down. There are full novels written on the topic of the half halt, and there are so very few riders who can ride a half halt to its full effectiveness. I've been practicing for years, and still don't feel that every one of my half halts connects. It is a forever growing learning curve to ride a correct half halt. In fact, I find it as satisfying to ride a perfectly executed half halt, as I do to ride a lovely half pass or pirouette!!!
A flying change is executed in canter, where there is a 'jump' in the gait. The horse changes lead from left to right/right to left, without breaking to trot or walk.
I suggest Bluebird that you talk to your instructor more thoroughly, and if he/she maintains that a half halt can ONLY be ridden in walk, or that a flying change is any alteration to any pace.... then find someone that knows the back end of the horse from the front, as this information is SO incorrect that it's not even amusing.