Possible on the flat spots. Also, some tires are not round which when tied in with wheels that have problems can cause that issue. Toss it up in the air and do some investigation. Tire out of round, cord separation, sidewall not true, wheel with the same issues. Some of the better brands of balance units will give you runout specs with max amounts. You can sometimes help on that by braking the bead on the tire to rotate it to a better location on the wheel. The machine will let you know where. If either are too far out, it's replacement time. Also check the axle flange and rotor wheel flange to eliminate them from the equation. Bent, studs not placed correctly giving you up/down issues. When I worked at the speed shop in the early 80's, my boss had chrome steel wheels on his Chevy dually. Had a constant vibration that couldn't get found with normal means. Turned out that the wheel center on one was the problem. Also on some balance machines, you can get road force balancing which is different than the norm. They apply a roller to the outside of the tire/wheel, when spinning, under a high load, which can make a difference on the balance.
At a shop I worked at before moving here, there were two customers who supplied repos tires for their rides. Two different suppliers and manufactures. Both vibrated. Some was due to the wheels having tolerance issues. They would not balance out and neither customer wanted to pony up to get new tires/wheels to fix the problem.