The short answer is NO. Unless you try to go over default brightness (which could potentially burn the LED), your screen leds are desgined for changing brightness and colors.
Leds work differently than most lightbulbs and flicker has much smaller effect on them.
Longer version of explanation
First of all, leds do not "flicker" the way fluorescent light bulbs do when they glow. LEDs glow by steadily releasing energy (photons) from electrons whereas most other light bulbs rely on heat to release light.
- Incandecent - These bulbs are literally a wire that's being heated and the light from that same wire.
- Fluorescent tubes - A bit too complex to explain in once answer, but in short, they rely on electricity to heat (basically) a wire that heats gas which in turn activates phosphor emitting the light.
A point to note here that both lamps heavily rely on heat to shine and in turn, breaking current could result in heating elements getting damaged
- LEDs light is emitted a little differently. Diode (the glowing bit of LED) consists of positive charged and a negative charged plates. When affected by electricity the charges are forced to mix, which causes electrons to release energy (light).
Flicker on most heating light bulbs damages their components
Now the reason I say LEDs don't flicker the way other light bulbs do is because other light bulbs mostly heat-up and cool rapidly during each flash. In addition to that additional heat may be inflicted on the heating component during a short reverse of phase occasionally happens on power breaks. To summarize, flickering causes the heating component to crack or burn out on standard light bulbs.
LED light emission doesn't rely on heat, also, if current is reversed (like it unusually gets on power cuts or breaking current) on LED it doesn't simply shine the way most other lights do - as in fact it pulls the positive/negative charge away from each other preventing a glow.
Flicker on LEDs
As far as i know LEDs can only flicker when electric current is too low to maintain constant mix of charges between the 2 semiconductors, which would result in burst exchanges every time diode is "charged" with enough electricity.
Flickering as well as dimming by itself is known to reduce the lifespan of an standard (room-lighting and small) LEDs by 30-60% (according to various sources).
Anyways, phone screens are designed to last while being dimmed and under changing current, so even if your screen suffers it will probably outlast the phone.
With that in mind an led with lower current might glow dimmer or change color, but the light-stream should remain steady - at least on screens.
If they DO flicker (I could not produce the flicker on 3 of my android devices), they are technically getting their lifespan reduced, but still not enough to matter.
LED screens (with everything they contain) are designed to be dimmable and most apps you see on the market are most likely just exploiting device settings.
If you can perceive a flicker it will reflect on your health more than it will on the phone. Be wary of unusual headaches or dry/tired eyes.
Easiest way I found to detect display changes on screen is filming the screen as you're changing the settings. If flickering DOES occur you should see it quite clearly in the video.