Despite a family history of breast cancer you can still safely complete a breast augmentation procedure. There is no information to suggest that breast implants will prevent detection or delay detection of breast cancer. Indeed patients who have had breast cancer can elect breast augmentation of the remaining uninvolved breast to improve symmetry and feel of the reconstructed breast. If breast cancer were to occur in a breast which had been augmented, the treatment and chance for cure would not be impacted, and, the extra skin envelop produced as a result of the the breast augmentation may be beneficial in reconstruction after mastectomy.
Breast implants do cast a shadow on a routine mammogram and it is important to notify the mammographer of the implant to obtain the additional views necessary to around the implant fully. The implant will not hide a breast cancer on an MRI study.
Augmentation in most patients is performed placing the implant under the chest muscle, pushing all the breast tissue forward. Breast self examination should be continued and will help with the early detection of an abnormal lump. Before augmentation you can consider a mammogram and should have a through breast examination. Your family history may not warrant genetic testing, though it is also reasonable to discuss this with your primary care physician or OB-GYN.
Your family history is a risk factor and just that. It does not mean that you will develop breast cancer. With knowledge and preparation you can be a good candidate for breast augmentation.
Best of luck,