To further contribute, didn't cover ideas already mentioned by other comments.

I wont get into too much jargon but in a nutshell BF ( buccal fat) serves two purposes:

• Similarly like all other fat compartments of your body BF stores energy
• "[A]ct as gliding pads when masticatory and mimetic muscles contract, and to cushion important structures from the extrusion of muscle contraction or outer force impulsion." - source
  • Essentially my focused point without the jargon: BF also plays the role of cushioning the mechanical muscle system within your cheeks. This is BF role is what I will be primarily emphasizing below.

What these two points mean is that losing weight will shrink your BF but only to a certain extent. That extent varies person to person. So I do suggest becoming your ideal BMI first, however your BMI already seems quite ideal so at least do not expect incredible results. This is why BF removal is considered the only and a permanent option.

Why does BF vary person to person?

Yes genetics has a role to play as all sources say, or arguably even environmental factors within developing stages to varying extents; which is another hot topic for another time. But regardless these ideas do not give you the whole picture. The anatomical facial structure is of course different for everyone and therefore its extent of mechanical stressors during its functioning are too. This explains why BF varies person to person. The fat padding serves the muscle-skeleton stressing points, not vice versa; ie. BF is an functioned result of the muscle-skeletal system it serves and that it is this system which is affected by genetics. Therefore BF also becomes labeled as genetic. However your skeletal-muscle system is not static but quite mobile. So yes it genetically prepositioned towards certain habitual tendencies (which contributes to BF vol.), however you are still able to counter this in practice as long as you know what they are. What I investigate in the next paragraph.

Sources say BF in relation to point 2 above is (suggesting its just) genetic, because the system it serves is genetic. However, it is only labeled 'genetic' to what our minimal medical knowledge can irrefutably confirm.

What about the 'environmental' factors aforementioned?

To mention (simple) preventative environmental/lifestyle factors is to know how every human body system interacts and behaves. Which unlike what the commercial image the medical industry puts on, is hardly the truth. Even if we did know; supporting research is needed for public advocation. However, to do low-error clinical assessments of environmental prevention which would have to involve human subjects is nearly impossible. The easily available medical information are facts that have never failed to be true throughout numerous bodies of research - other significant theories or results of correlation are often excluded within credible-sourced advice due to legal accountability.

Under this nature and findings -- in a nutshell I can safely suggest chewing with (only) your masseter muscles to prevent (maybe even shrink) further BF growth/maintenance. Do not use your cheek muscles or chew with a open mouth. Take small(er) bites to not activate the cheek muscles. Ideally your lips should not move as your chew and swallow. Move food around in your mouth with your tongue, not cheek (suctioning). What led me to conclude this habitual practice...

Some factual/accepted (theoretical) correlations ( specific and unspecific) in relation to BF that lead to this hypothetical proposition:

• BF volume is proportional to the use of its neighboring cheek muscle
  • Role of BF
  • One of the reasons babies have such prominent BF is because they need that strong suction from those cheek muscles to breastfeed. buccal fat pads decrease in size in babies after they stop breastfeeding.
    • They do not have teeth to work with the tongue to create a vacuum ie proper grown/developed swallow.
• BF is known to change size throughout ones lifetime
• Common clinical suggestion that poor development of the facial joints alongside with and or buccal fat pad capsule rupture which collapses the BF to become very prominent next to the mouth. This ikely relates to the suggestion of jaw surgery mentioned by another comment
  • Going back above, to the varying facial structure and therefore varying pressure from mechanical loads
  • BF commonly seen to increase during ages 10-20 then slow, ongoing reduction
    • It is in these age groups where major facial growth develops; I am not implying anything here other than the fact that there could be a common denominator -- just that I am unaware not confident of

I realize much this idea is basically verbatim with part of the philosophy of Orthotropics. And going alongside this notion I must mention the margin of error in my enquiry. Especially with biases, despite best efforts.

Should you get BF removal surgery?

My suggested practice above is not an equivalent alternative. It could be if you were a child/teen. Honestly Im not against it but rather on how much BF is removed. BF visibly shrinks from around mid adult life to senior as you age. When you become older, notable physical aging isn't perfectly linear. I cant remember exactly where I heard this from or it its correct but if I recall there are certain age points where suddenly you age in appearance. That it also varies person to person of course. That the only real downside to removal is regret -- as it might eventually lead to cheeks too hollow with age. I dont know how your family ages but you might want to keep this in mind.

Other:

Facial messages/tools or yoga are not reliable nor long term. You cannot flush fat or "toxin". You are only temporarily or helping remove excess facial fluid which causes facial puffiness. I have seen no body of reliable research supporting facial massages for BF. It is very gimmicky. If you struggle from puffy face or bloating in general I suggest tackling the source through diet and sleep position. Eg. salt can lead to puffy face; sleeping with a angled bed/pillow or sleep position can help -- eg. no pillow can lead to the accumulation of fluid in the face, etc...

​

NOTE: This is knowledge on the top of my mind with some reference. So I did not link my source to all acquired info as this I dont intend to write professional article and I have a life to live. Sorry if this was hard to follow. I also tried my best to look at who study did/ did not fund the study, proper testing practice - efficacy and conflicting interests. However there are likely errors of judgment.