If my parents had leg claudication, does this mean I will too?

Net necessarily. The three greatest risk factors for claudication are 1) smoking, 2) age, and 3) diabetes. Family history by itself is not the greatest risk factor. You can minimize your chances by making sure you don't smoke, and stay on top of your diabetes if you have it.
IC. Claudication not hereditary. Do not smoke, eat healthy, regularly walk and manage BP, blood sugar and cholesterol and you will lower your risk of developing Claudication or other atherosclerotic disease.
No. Claudication is a form of peripheral vascular disease. The risk factors are smoking, hypertension, diabetes and high cholesterol levels. Genetics has a lot to do with this as well but you need to concentrate on the risk factors and decrease your risk.