There's a difference between flicker, shimmer and strobing. The type of flicker that makes a pen look like repetition of ||||||| pattern when you swing it across rapidly in front of the fixture is almost always caused by the design of the LED ballast. Many consumer grade LED fixtures can be easily disrobed until you can see the LED elements. Many of them will be just a thin disk 2-4 inches around sprinkled with LED elements. These are pre made "bolt-on" LED light-engines made available to fixture manufacturers by various China manufacturers. Energy Star listing has no real meaningful requirements on flicker, so they're still able to earn the label. If you don't see a capacitor much larger than a match-head on the LED board, then you've found the answer.
Is the "flicker" similar to the way Christmas lights look like in their steady-on setting?
Capacitors used near the LED lamp elements run hot and they're often the point of failure, so fixtures designed without a capacitor have improved durability and power factor issues by ballasting the LED with a semiconductor chip driver and no capacitor, but there's no getting around the flicker on 60 Hz power without significant capacitance on the electrical or optical side (glow in the dark).
Most "LED light bulbs" have a capacitored ballast with a shorter expected lifespan than a permanent fixture, but replaceable bulbs do not have the same expectation of lasting the lifetime of the fixture. Since you can't swap out the LED engine without invalidating the UL listing of the entire fixture, the only solution is to get a different fixture and do the "pen test" while still in the show room, or at least before it is installed.