Opinions on actual chemical process that occurs with Kybella injection as it relates to the inflammatory response?

This is really a great question. As we continue to use Kybella, we are learning that it not only causes destruction of the fat cells, but skin tightening through the inflammatory process which occurs. Those compounds you mentioned do not affect blood supply, but rather reduce the inflammatory response. 
No one has real data on this issue, but I do think the inflammatory response helps tighten the skin. That is why I tell my patients to not ice the area, and to allow the inflammatory process to take its course. 
This is purely my opinion, and I only have my intuition and anecdotal patient data to support this. I do think that the swelling ultimately is sacrifice that produces the best results. In my experience, the patients that usually have the most swelling have more dramatic results. I don't want anything to interfere with that process.
Hope this helps.

Part of the results of Kybella, especially the skin tightening,  are as a result of an inflammatory reaction created by the patient.  Therefore, it is recommended not to take any anti-inflammatory medication after treatment with Kybella.  I tell my patients to use ice as much as possible for the 72 hours after treatment in order to minimize swelling.

This is an excellent question!  Kybella is made from deoxycholic acid - a naturally-occurring detergent compound that ruptures and destroys fat cells on contact.  The effects of deoxycholic acid on fat cells occur almost immediately after injection, which is why patients often experience a burning sensation during treatment.  The inflammatory response and swelling that occurs afterwards is due to the body's attempt to remove the dead fat cells from the area after treatment.  While it is unlikely that NSAIDs or or other anti-inflammatory medications would dramatically reduce the extent of fat reduction, many injectors feel that the secondary inflammation plays an important role in tightening the skin after a Kybella treatment.  I don't believe this has ever been tested or shown in a scientific study, but as a result, it is often recommended that patients avoid taking anti-inflammatory medications after Kybella.  I have recommended short courses of oral steroids for patients who are very concerned about post-Kybella swelling, and I don't believe it has dramatically impacted their results.  I hope this helps!