Can I use natural progesterone if there is family history of breast or uterine cancer?

Yes, it is recommended. Breast cancer and endometrial cancer are two cancers that are related in some way or other to gonadal hormones. They occur in tissues sensitive to these hormones. Unopposed estrogen is the only known cause of endometrial cancer though there may be other factors involved. Estrogen, or at least one or more of the various estrogens, are thought to contribute to breast cancer.