What is the risk of infection with a Brazilian butt lift (BBL)?

In published studies, the risk of infection from BBL is quite low- less than 1%. The risk in putting in implants for butt augmentation is much higher- about 3%. Infection would likely be caused by natural skin bacteria. 
What is more likely to "kill" any transferred fat is the unpredictability of fat transfer. This is still being extensively studied by plastic surgeons, though many are still achieving great results. 
Please make sure your surgeon is trained in plastic surgery and is board certified or board eligible by the American Board of Plastic Surgery to ensure maximal safety and effectiveness for your procedure!

Thank you for your question. Infections are not usually seen within my practice, but there is a list of protocols to be followed to prevent them (as all Board Certified Plastic Surgeons in the US should follow). As infections are a risk that you take with any surgery you will ever have.  Antibiotics should be given during surgery and for the post-operative period until incisions have healed. Infections are however a risk that you take with any surgery you will ever have. 
Ensure that you are following all protocols as instructed by your surgeon. I wish you the best of luck!

Fat embolus is a very serious and known complication of fat transfer (which has been recently spotlighted in the media). While it is true, injection of donor fat into the infra-muscular plane (within the muscle) increases fat viability this does come with a significant increase in risk. There are large vessels deep to and within the muscle which can be inadvertently injected while grafting leading to a fat embolus. The consequences of such a complication are very serious and life threatening.
At the recent American Society of Plastic Surgeons Hot Topics (2016), data from AAAASF (ambulatory surgical certifying body) was presented, suggesting that BBL/gluteal lipoaugmentation demonstrates a dramatically higher risk profile than other surgeries. The Aesthetic Surgery and Educational and Research Fund is convening a task force as well. The hope is that we will have more concrete guidelines for addressing these very serious complications.
That being said, the safest way to avoid fat emboli is to stay in the subcutaneous plane (at the expense of fat viability)and avoid the deeper muscular plane. If grafting of the deep plane is planned, surgeons should consider blunt cannulas, aspiration prior to injection. Using a supra-gluteal approach to minimize the risk of inadvertent intravascular injection has also been proposed. While this will likely impact graft viability negatively, it will also lower the risk of a serious complication.
With regards to your specific question, according to AAASF data the risk of death from BBL will range from 1:3000 to 1:6000 (subcutaneous grafting will reduce this risk relative to intramuscular grafting). By comparison the risk of fatal complication from abdominoplasty is 1:13,000. There is very little data regarding infection. In my experience, the risk of infection from SAL and fat transfer is fairly low. These risks are generally managed via perioperative antibiotics and sterile technique (as the most likely pathogens are skin contaminants).
In summary, the procedure can be safely performed, however, they should be performed by a board certified (ABPS) plastic surgeon with experience. These risks should be discussed as well as the strategies being employed to avoid them.