Can an external tissue expander over the breasts kill fat cells?

You are mixing information about internal and external tissue expansion. Internal tissue expansion will cause some thinning of tissue over the expander (but doesn't necessarily kill fat cells). Also external expanders are only used in the setting of later fat grafting. You will not achieve any results from using the expander alone.

The Brava suction device you are referring to never worked. I put it under the category of wishful thinking. It had been tried fir years and found to be useless. I don’t believe it’s even available anymore.

Brava was conceived of and originally produced as a means of permanently enlarging the breasts by applying frequent intermittent suction to the breasts. Typically 8 hours a day for a month or more. Keep in mind, you cannot hide it under clothing. After extensive testing, average breast enlargement after using it for months at a time was less than 100 cc, or about two thirds the size of the smallest breast implant. There was no long term follow up to confirm efficacy past 6 months. One of the inventors, Roger Khuri, M.D., went on to pioneer fat transfer to the breast, incorporating the Brava system as a means of optimizing the breast tissue for fat grafting. My suggestion is either fat grafting of implant based breast augmentation.