There is a chance but Down syndrome is hereditary in approximately 1% of all instances. In the other 99% of cases Down syndrome is completely random and the only known factor that increases the risk is the age of the mother (over 35). Translocation is the only type of Down syndrome known to have hereditary link. Translocation accounts for 3 to 4% of all cases of Down syndrome. Of those, one third (or 1% of all cases of Down syndrome) are hereditary. - See more at: http://www.ndss.org/Down-Syndrome/Myths-Truths/#sthash.XIEz47Qw.dpuf
There is a very minimal chance but if you want to be sure, just have your baby checked and take it from there.
I found out my daughter likely had down syndrome during the first ultrasound where it revealed several heart deformities. I did not have any further testing because honestly we already loved her and she was our baby and she was perfect.
I do not believe there is any genetic link to down syndrome. I have a daughter with DS and nobody in either her dad's or my family has ever had it. I understand the fear of the unknown, but honestly there is nothing to fear.