Small chance. I'm a family of four and my mom got serious freckles and not one of my mom kids had them.
Freckles occuring are hereditary, but whether you'll get them and how many you'll get depends on sun exposure and the fairness of your skin, and even whether or not you appropriately use sunscreen.
There's a chance, but it's probably pretty small. My mom is covered from head to toe in freckles and I barely have any at all. Dad has some freckles too. I don't think it's hereditary? But I don't know for sure!