Fat distribution after Brazilian butt lift?

Fat NEVER "travels" or redistributes itself, even after surgery of any kind. When fat is removed from any part of the body, those fat cells are gone, and only the fat cells left in the operative site can be "fed" by additional weight gain. So let's say that you had liposuction of the hips, and your surgeon removed 50% of the fat cells in your hips. Good job, if things were removed smoothly, with nice transitions rather than a big "shark bite!"
Now let's say you get lazy and gain some weight. Your fat cells do not know that some of their counterparts in the hips have been permanently removed. The fat cells in your belly, butt, breasts, etc. are all still there, but your hips have 50% fewer cells to receive those extra calories in the form of fat cell enlargement. So your belly, your butt, your breasts, your etc. all get "fatter," and so do your hips--BUT, your hips have 50% fewer cells to enlarge, and therefore do so less than these other areas. This leads patients to say, "Lipo doesn't work, that fat from my hips just 'went to' my belly, my butt, my breasts, my etc." The fat didn't "move" "travel" or "redistribute" in any way. You simply got fat again and put it where you had all of your fat cells present.
Over time and with the hormone changes associated with menopause, you did indeed see fat distribution patterns shift. But not because fat "traveled" or fat cells "grew" in certain areas and not in others. It's too complex to summarize in this forum, but suffice it to say that hormone changes cause the metabolism of fat cells (all of them slightly different in different areas of the body, and why some people get fat bellies and keep skinny legs, and others see huge thighs and still-slim bellies, etc.) to absorb fat in different ways than when the hormones were more active. So over time, you did indeed see the absorption of fat change from hips and thighs to your belly. But not because the cells or the contents of them "went on a trip!"
So if you undergo a BBL, liposuction will take some of your belly fat (and perhaps from other areas as well, as you and your surgeon decide) and mechanically remove it (permanently) from those areas and literally transplant it to your buttocks, where 50% or so will survive. This means your belly is smaller, and your butt is somewhat larger. If you maintain your weight with diet and exercise, no fat will "move," "travel," or "redistribute" in any way, ever.
UNLESS you gain weight, in which case the fat cells that exist in each of those respective areas will enlarge. So your bigger butt will get bigger, but so will your belly, breasts, hips, etc., according to the number and distribution of the then-existing fat cells in each of those areas.
But if you're like the majority of Americans, your after-menopause slowed metabolism and your tendency to overeat will conspire to make you fatter, and your fat cells already have a personal hormonal receptor tendency to collect those extra calories in your belly slightly more than the fat cells in other areas. But, remember, fat does not travel unless it is mechanically (via BBL) transplanted to your butt.
The good news is that your butt now has belly fat cells, whose hormone receptors have the tendency to "receive" fat just like the donor (belly) area. So if you gain weight, your belly's remaining cells, AND your butt's new transplanted belly cells will enlarge.
But no fat cells are going to move. Only your intake and calorie burn (diet and exercise) will determine what gets fat and what doesn't! Hope that is as clear as mud! Best wishes! Dr. Tholen

No fat does not travel around the body. If you gain or lose weight the fat cells in any particular area will get bigger or smaller, but the proportions stay the same. Fat redistribution is actually a myth. I have done a study on this phenomenon using photometrics. This is a good thing because otherwise having liposuction would probably be unwise. You can read more about this at my website. The link is below.

Patients will commonly wonder what the effects of liposuction will be on their weight and more specifically their ability to gain or lose weight in treated and untreated areas. 
After puberty, an individual will have the same population of fat cells for the remainder of their lives (barring an intervention). Any changes in weight will manifest not as more or less fat cells but rather swelling or shrinking of those very same fat cells.
Liposuction destroys or reduces the population of fat cells in a treated area. These cells once gone are gone for good. The treated areas now harbor a reduced population of cells and consequentially have a reduced potential for weight gain or weight loss. However, a reduced potential does not make changes in these areas absolutely impossible. The remaining cells can still swell with weight gain potentially compromising a cosmetic result.
The final component is the least understood. This is that of weight/fat distribution. It remains unclear how the body directs particular populations to change. Patients will often lament that attempts at weight loss are frustrated by losses in areas not targeted and weight gain by contrast goes directly to perceived problem areas. It is impossible to predict how a patient will respond to weight gain. While we know that treated areas must theoretically have a lower potential for growth by virtue of reduced adipocyte populations, this does not necessarily always hold true with some patients always demonstrating the effects of weight gain in the same predictable areas. Similarly, post operative weight gain is not always manifested in untreated areas.
The best advice one can give is to reach a stable healthy weight pre-operatively and try to maintain post-operatively. This is the best way to achieve a good result with the best chances for longevity.
As always, discuss your concerns with a board certified plastic surgeon (ABPS).