Are Black women more prone to liposuction burns? Or is it fully based on the doctors technique and negligence?

The color of the skin has no relationship with Liposuction burns at all.
Burns are more related to the use of energy-based-liposuction or aggressiveness trying to remove the majority of the fat. No doctor will ever try to burn a patient on purpose.
Dr. Cárdenas

It depends on what you are considering a "lipo burn". If you mean an actual burn to the skin where skin has damage etc. then this is fully up to the surgeon's technique and not more common on black skin. It is more common with energy devices such as laser/vaser where heat can burn the skin and aggressive lipo cannulas such as baskets. If you mean hyperpigmentation or PIH (post inflammatory hyperpigmentation), then yes this is more common on darker pigmented skin including African American, Asian, Hispanic, Middle Eastern, etc. This can occur with just the trauma of liposuction and causes pigment to collect in the skin overlying the areas of lipo, especially where it is aggressive like the waistline with a BBL. Similar to pigment that collects when you get a bug bite or pimple.