Lighting, Light Fixtures, Ceiling and Exhaust Fans - recessed lights flickering and burned out applicance

I have recessed lighting in my bathroom. The home was built in the 70's with remodeling done in the late 90's early 00's. When I use a certain electrical appliance in this room, the lights flicker. Additionally, the applicance has burned itself out 3 times in the last year. The company keeps sending me a new one since it is under warranty, but its annoying and I can't help but wonder if its burning out because of the wiring in some way. The appliance is a hair straightener that claims to be ionized. The lights flicker when I squeeze the plates together to straighten my hair. I hope I've explained this enough. I know it sounds strange. Why are the lights flickering and why is the appliance burning out?

When incandescent lighting in on the same circuit as any high-current appliance, such as a vacuum cleaner, a clothes iron, a hair dryer, or a hair straightener, the lights will always dim. The dimming, however, should be more towards the slight end of the scale than the severe end. If you have severe dimming, you may have a loose connection on the circuit which should be corrected before it causes a fire.

The burning out of your hair straightener is probably unrelated, and a function of the design of the appliance or of how you are using it.