Hi OP!
I work for a an aesthetic practitioner so we do procedures all day every day, however ONLY procedures that actually WORK and look good (and natural.)
A Botox lip flip will not add any volume to the lip as you requested. Moreover, Botox lasts about 3 months maximum. In the mouth area where you are constantly using the muscles, this is unlikely to last much time at all. I’m not sure why it’s even called a lip flip or even a lift, it does very little other than temporarily paralyse the top lip and philtrum which makes it hard to smile and can often give a constipated appearance.
Botox temporarily paralyses the muscles injected; so it works well for frown lines and light wrinkles but really not so well for lifting anything significantly or naturally. Lip lifts rarely look good, even when surgically enhanced.
You are, however, absolutely capable of achieving subtle volume and lift through lip filler as long as you go to the right practitioner. Make sure 1) they are MEDICALLY TRAINED AND INSURED (Doctor, surgeon or a nurse) 2) you can actually see the work they have done and make sure you like their style!
I can guarantee you would be happier with the results of a great lip filler procedure than Botox to achieve your goals!
Best of luck!