The person: what’s their approach to the matter. We cannot generalise since this a personal approach to an individual life. Bach flower remedies are not like chemical medicine where the substance is an alterative which will affect you whatever the condition. In some cases the most important factor is the attitude of the person. It may be important to be self-aware. But then that is not applicable if the patient is a child or an animal. So it all depends upon who the person is.
If there is to be a single important factor then maybe it is the attitude of the person who is administering the remedies. They should try to be of service and not impose dogma or restraint upon others.