Is it ok if i did mamogram and three months later i had a chest x-ray for my residency . will that increase my breast cancer or lung cancer risk ? is there any food or supplements that i can take to reduce radiation in the body ?

Medical imaging tests such as Chest X-Ray, and Mammograms are considered safe even if used repeatedly. This is because the dose of radiation delivered to your body is too small to cause harm or increase the risk of developing Cancer. So you can safely have repeat testing(even when larger radiation dose is delivered as is the case with the use of CT scanning).

The amount of radiation you mentioned would not raise your risk of cancer above your background natural risk, You can reduce your risk of cancer by adopting healthy habits: Eat a mostly vegetarian diet, avoid alcohol, tobacco and street drugs, avoid excessive exposure to sun, get HPV vaccine, exercise 30 minutes each day, drink enough water so your urine is mostly colorless.