A lot of "dimmable" LEDs are actually shifting the flicker pattern to dim the light (shorter on phases). This is for LEDs where the user dims per remote control. OP was talking about the older "legacy" dimming, where you have a wall-mounted knob that reduces the current. Works well with incandescent bulbs. But only few LEDs support this. If they do, their internal power converter likely won't flicker, because of their more thought-out converter?
However, there are also LEDs that support legacy dimming, but again translate less current into different flicker patterns...
I've been trying to switch to all-LED in a home with lots of legacy dimmers and it's been painful. Even on circuits where I've replaced older dimmers with new Lutron CFL/LED dimmers, I get flicker.
In other places I don't have dimmers but have low-voltage (12V) cans. Lots of flicker issues there too, presumably due to the 120->12V transformer at the can.
And then I have a light fixture that's both dimmed and a custom 12V setup. I've given up on finding a working dimmer/LED bulb (MR16 GU5.3) there. Probably need new 12V transformers?
However, there are also LEDs that support legacy dimming, but again translate less current into different flicker patterns...