Is coughing up a red phlegm mucus wad normal after a breathing tube & surgery?

You are correct in that the bloody mucus is likely related to the use of the endotracheal tube during your procedure. However, always best to run specific concerns by your plastic surgeon. Generally speaking, careful attention to respiratory care ( ambulation, deep breathing, coughing etc.) is an important part of the postoperative regimen after “mommy makeover” surgery. These measures will help prevent potential problems such as atelectasis and pneumonia. Best wishes.

What you describe is not totally out of the ordinary but should be getting better. I think you should report this to your plastic surgeon.

You are probably correct that this is from the tube that was placed in your throat during surgery.  You did the right thing by reaching out to your plastic surgeon just to make him/her aware of the situation.  If it was just blood tinged mucus it is likely from irritation.  If it was a significant amount of blood you will want to report that.