Tummy time?

My son is 5 weeks old and I am starting to worry he isn't getting enough tummy time. Usually every time he is awake we play in his activity gym and he wriggles around and grasps / bats at the hanging toys for about 20-30 minutes or so. But because he has such awful reflux I feel terrible flipping him over to do tummy time because he ends up spitting up and crying. We can maybe get in 2-3 5 minute sessions a day, because I only do it once per play time and then he is crying and wants to be picked up. How often is everyone else doing tummy time? And do you have any tips for reflux babies? TIA!