Flat Iron Causing LED Lights to Flicker
this happens when LED bulbs don't have proper (or any) DC conditioning. Cheaper decorative LEDs in the US use a simple circuit of ~50 LEDs in series, with no other regulation. This also means they are off half the time (60 times a second they blink), but some bulbs will have multiple series strands in reverse polarity, so that at least one "filament" is lit the majority of the time and the flicker rate is doubled to a less-noticeable 120Hz. 

These styles of bulb are extremely simple electrically, literally about the same as a tungsten bulb. They are nice and pretty and cheap to produce, but they doesn't work very well. Small fluctuations in voltage will have large effects on the light output because the LEDs are unregulated and being driven close to their limit. Unlike tungsten, which has a linear voltage-to-lumen ratio, LEDs produce exponentially more light with voltage above their specification. So while a 2v dip on tungsten might decrease light ~2%, it can cut the LED's ouput by ten times that or more.

You want a more expensive bulb that will properly convert the incoming AC to lower-voltage DC to keep the output steady over a wide variety of input voltages. If there's a short delay from when you turn them on to when they output light chances are they won't flicker no matter what you do.