Although this might make its way to first aid training one day, it would likely fall within the realm of “athletic first aid” as oppose to “standard first aid.” To my knowledge, most personal training certificate requires a trainer to have standard first aid or better (e.g. first aid for health professional). Unfortunately, athletic first aid does not meet or exceed the qualifications of standard first aid.
The reason is due to the application of the first aid. Standard first aid and first aid for health professional forces the giver of first aid to patch up the trouble spot long enough for a medical professional to take care of the situation. In other words, the person receiving first aid would have to cease their activities. On the other hand, athletic first aid patches up the athlete/player long enough to get through their activity (thus seeking medical attention after the activity is done).
The use of k-tape (and the like) is to enable a player to do their activities while injured (something that a personal trainer should not be doing without obtaining clearance from a medical professional). Even then, the trainer should not be the one putting on the k-tape on the clients. If the client is prescribed k-tape, then they would have received the training to put it on themselves and should have it on before working with a trainer.