Please tell me if you can get periodontal disease from brushing once and flossing once a week?

Very Possible: The less you take care of your teeth, the more the chances of loosing them. It is suggested that you brush twice a day and floss once a day to maintain a healthy mouth. At once a week, you may not be doing much at all to help the situation. Please consider increasing the frequency to give your teeth a chance to remain in your mouth.

Yes, most probably: A lack of good oral hygiene is a major risk factor for developing gum disease. Make a habit of brushing and flossing after every meal.