Concern has been expressed that the children of women who have had silicone breast implants are at higher risk of certain illnesses.

This is not true. 
In particular it was suggested that congenital abnormalities, rheumatic diseases and esophageal disease may be more common among children of women with implants. 
Fortunately current research shows there is no good evidence for this and that studies among Danish women show no increased risk to their children.