How does high blood pressure affect facial fat transfer and it's ability to attach to new capillaries?

There is no medical evidence that any changes in blood pressure affect how well fat grafts take. This is certainly true for high blood pressure where perfusion pressures are high. It may be different in low blood pressure but then one would have other more important problems.

High Blood Pressure has very little influence per se on revascularization of transferred fat. It could, however, increase the risk of bleeding from the injection procedure and that could reduce the revascularization since the blood would act as a barrier to the new vessels getting to the fat cells. For this reason, you should make sure that your blood pressure is totally stable and within the normal range before having the procedure.