The unique design of The Better-Fly allows it to grip onto your arm with its interior rubber lining. The innovative BUCKLE allows the strap to be tightened to increase contact with your arm, but the BUCKLE is NOT meant to make contact with your arm or leg. If it does, you need to loosen the buckle or change the angle of the cable.
The main thing to remember is that any new device takes time to learn and understand. Various cable angles and standing positions will alter the effectiveness of the grip and the stability of the device. If you are encountering movement up or down your arm, adjust the buckle or the device's position on your arm or leg first, then adjust the pulley position of your cable machine, then adjust where you stand in relation to the the pulley.
By experimenting with these variables, you will find a position where The Better-Fly is secure and remains in place throughout your range of motion.