How long for axillary folds to disappear or significantly shrink? (Photo)

You have to remember that it takes time for your body to heal.  You are just 1 month post surgery. I tell my patients that the first 3 months about 60% of the swelling is gone and at 6 months all the swelling should be resolved, sometimes it does take longer.  Make sure you speak to your surgeon with any concerns you may have. Best of luck.

Dear Veronica919,I understand your concern and it is quite normal to be concerned about the outcome following a breast reduction surgery. However, you are still in the very early stages of the healing process.Your will need to be patient at this moment and follow what your surgeon has instructed you to do post operatively.At the early stage of the healing process, the tissues are still swollen. Once the swelling subsides  you will be able to see the final result of your surgery.Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery

Hi and welcome to our forum!
From the photographs, I see the residual fullness about which you are concerned. 
The surgical procedure was traumatic to the soft tissues, which will result in swelling which may totally mask the surgical result for at least 6 months or longer. 
I recommend continued followup with your surgeon. Express your concerns.
Best wishes...