Mammograms can sometimes still be indicated when a nipple and skin sparing mastectomy with implants are done to reconstruct the breast. However, if the entire breast tissue is totally removed, and the chest is totally flat, then there is no way that a mammogram can be done (since there are no more mammary glands in the first place).
A good option to monitor recurrence is for regular physical examination, taking into account skin and muscle changes in the chest area (with serial photographs if necessary for a more objective comparison).
Having had a separate incidence of breast cancer in each breast only 3 years apart, have you ever been tested for a BRCA mutation? Do you have any family history of cancer, particularly breast and ovarian? If so, it might be worth your while to meet and talk with a CERTIFIED genetics counsellor about testing.
I can totally understand your worry about possibly stopping mammos. If mammos are not possible due to being flat, would MRIs be an option?
And if its some consolation, while another lump may still possible even after mastectomy, I believe the risk of this happening is very low.