What will Lidocaine do for blood flow ?

Hmm.  In my opinion lidocaine three weeks after the surgery will not do much but numb up the skin.  Lidocaine can cause the size of blood vessels to increase thus increasing the circulation.  This usually placed directly on the blood vessel at the time of surgery.  This technique is used when transferring tissue and reconnecting blood vessel NOT for breast reductions.

Are you certain your doctor prescribed lidocaine? Lidocaine itself actually has no effect on blood flow.  Nitroglycerin paste, however, is sometimes prescribed to increase blood flow after breast reduction.

I am not sure why your surgeon would suggest lidocaine other than perhaps for an anesthetic at this point.  Local wound care probably would help an open wound.