I bought 4 different brands of LED bulbs off of Amazon and tried them out. Currently, I only have slo-mo phone camera for testing, but am working on an oscilloscope solution to get better results. With slo-mo camera, I can detect flickering (from AC current) in my incandescent and halogen lighting for control. I notice that some LED bulbs flicker similarly to incandescents and some flicker much more sharply. Below are my findings on four brands.
Energetic PAR38 3000K- I detected no flicker with slo-mo video. It's not a perfect test and I wish I had an oscilloscope, but it's the best I can do at the moment. I figure if I can detect incandescent flicker and nothing on these, then it's reasonable to deduce that they don't flicker at all. I only tried their PAR 38 bulb but would hope that their other bulbs would have similar technology. They also make an A19 bulb. My only beef with Energetic is their warmest bulb I can find is 3000k. I prefer warmer light indoors. However, I do like this cooler/whiter light for outside and I'm going to put these bulbs around the exterior of my house.
Sunperian BR40 2700K - On this one I could detect flicker, but it was very similar, if not the same, to the flicker of incandescents. Interestingly, when you turn this bulb off, it "glows down" like an incandescent. You can see it slowly get dimmer and dimmer before turning off. It "glows down" more slowly than the incandescent bulbs that were right next to it. So, my thinking is that they have introduced some technology in LED bulbs to have them show some afterglow just like incandescents when the power to them is cut. If this afterglow also takes effect with the oscillating AC current, then I would expect an oscilloscope wave for these bulbs to look similar to an incandescent's wave and MAYBE be ok on our eyes and heads. I didn't love the color of this bulb either, they call it a 2700K but it felt more like 3000+K to my eyes, that's all very dubjective though.
Torchstar BR30 3000K - This one behaved very similarly to the Sunperian above as far as flicker. It MAY have been a slightly sharper flicker than Sunperian's but that's really hard to know for sure just using video. Even though this bulb is a 3000K, it felt slightly warmer than Sunperian's 2700K. I would like to try a 2700K version of this bulb for a bit of time to see how they feel with long-term use.
Sunco BR30 2700K - The Sunco bulb displayed a very noticeable, very sharp flicker. It is noticably distinct from the flicker of incandescents and the other 2 LEDs. I suspect that it would show the blocky waveform of the instant on/off oscillation that many LEDs do. This one also seemed to strain my eyes right away and I imagine would give headaches with any prolonged usage.
Energetic - Seems good and usable
Sunperian - worth trying
Torchstar - worth trying
Sunco - Stay away
I'm also going to try Greg's recommendation above. Thanks @GregAtkinson for that info!
Next step is to find/build an oscilloscope of my own and test more bulbs.