In North America, most name brand light bulbs are powered by a bridge rectifier, a smoothing capacitor and then a linear regulator in series with ~ 120-150V worth of diodes. Or at least every one I have bought at a Home Depot worked like this. The bridge rectifier and smoothing capacitor output a nominal ~165V peak with some additional volts of ripple. This ripple is dropped across the linear regulator resulting in uniform, ideally flicker free LED power.
This setup is not very efficient, but it is very cheap. The inefficiency comes because the voltage dropped across the linear regulator is directly converted to heat. The larger the voltage across the regulator the more resistant the lights to flicker but the more heat and lower lm/watt. If the ripple on the lines (due to both the 120 Hz from the bridge rectifier, any external noise on the lines, and any voltage droop on the mains) causes the linear regulator voltage to drop to zero, the regulator will enter drop out, and the LED brightness will flicker.
For example, I have a pretty good, flicker resistant LED bulb here that is composed of 7 SMD packages each with an 18V forward voltage (3v*6 junctions). That is 126V. The rectifier outputs 165V with maybe 10V of ripple, so the lowest voltage for nominal 120V input is 155V, while the LEDs will stay lit for any voltage above ~126-127V. That means I have 27V of head room, and any noise/droop/etc on the lines less than this will have no effect on the diode brightness. However, you can also find bulbs with smaller capacitors or less power wasted on the linear regulator that only have 10 or 15V of margin. These will be much easier to make flicker.
My guess is that if you probed your mains power, you would find that it is a few volts below nominal 120Vrms and there is probably some additional noise from a large load somewhere else in your area. The combination of these effects causes occasional cycles in which the RMS voltage dips by more than the voltage drop across the regulator, causing periodic variations in LED power which you see as flicker. This is only a guess, but I have seen it happen in practice.
If this is the problem, your best bet is to simply try a few other brands of light bulbs. A slightly higher voltage drop across the linear regulator or a slightly larger smoothing capacitor will make a large difference if you are riding right up against the regulator dropout voltage.