Is there anything that can speed up the healing process of fat necrosis after breast reduction surgery?

As your surgeon has stated, it will heal naturally. The best thing you can do to help the healing would be to prevent infection by keeping the incisions clean and dry. Antibiotic creams may be used but medication will depend on your surgeon's protocols. He ill be your best resource for information.

 I am sorry to hear about the complications you have experienced. How long it will take to heal will depend mainly on status/size of the unhealthy underlying tissue.  If the area of fat necrosis is small, it may take a few more weeks;  for larger areas, several months of drainage may be ensue. 
The important part of this process is close follow-up with your plastic surgeon, who may able to help with judicious debridement debridement ( surgical removal of unhealthy tissue).  Whether or not surgical intervention is indicated is a clinical judgment that only he/she can make after physical examination and consideration of your progress/concerns.
Best wishes for an outcome that you will be pleased with long-term.

Hello and thank you for your question.   Wound healing complications are not uncommon after breast lift or reduction. I advise you contact your plastic surgeon for his/her recommendation.  Best,
Jon
Ver Halen, MD FACS
Harvard
educated plastic surgeon
Texas
“Top Doc”
RealSelf100
America’s
Top Plastic Surgeons, Consumer’s Research Council