What is the healing process for lipo burns? (Photo)

Hello and I am sorry you are going through this complication. Based on the picture those look like quite serious burns with what appears to be skin that is severely damaged and even dead- known as skin necrosis, though an in person evaluation would be needed to be sure. This amount of skin damage is quite unusual from liposuction alone. Sometimes the skin around the site of incisions can have some minor injury from the friction caused by the liposuction cannula. Or, if the liposuction was extremely aggressive and superficial significant skin injury could occur. However, this amount of damage is rare for routine liposuction in my experience. 
The surgeon who performed the procedure should see you immediately and manage this complication. If the skin is severely burned, as it appears to be, then a surgery is likely required to remove the dead skin followed by wound care and/or skin grafting. If the skin is not as badly damaged as it appears then wound care alone may be sufficient, though it would take some time to completely heal and may leave significant scarring. If your surgeon is unable to see you then being evaluated by a burn surgeon would be an appropriate next step to offer you treatment options. 

 Thank you very much for your question.  In order to answer this question it is essential to know what kind of method the surgeon was using to harvest the fat. There are a number of ways lipo machines  work. Some of them to work with heat. This can essentially also burn the skin if the heat is applied too long at one spot. A burn can also occur can around the incision due to friction.  Regardless of what the cause of the burn is, it will have to be treated properly by, preferably, the same Doctor who did the liposuction. The treatment of burns as much as the time it takes to help burn depends on the severity, meaning its depth.  All the best for your recuperation. Have a wonderful rest of the day and greetings from the beautiful island of Jamaica.