I have noted that primary Alkaline batteries are 1.5V and the chargeable NiMH batteries (Includes the new GP Recyko+) are 1.2V.
Is this means that using the chargeable NiMH batteries instead of Alkaline in a LED flashlight, can improve the LEDs life in the flashlight because the input voltage is lower?

Depend on the used driver circuit and the exact alkaline design, but it may be worse.

Alkalines have higher open circuit voltage (so the initial LED current may be higher), but they have mostly higher internal resistance then NiCd or NiMh. This higher resistance play an important role in thermal stability of the LED's:
As any semiconductor diode (so include LED) forward voltage decrease with higher temperature, the setup tend to be unstable with the lower impedance voltage source (higher temperature cause lower diode drop, what force more voltage on serial resistance elements, what increase the current, what increase the power dissipation, what increase the temperature further,...).
So here the higher internal resistance make the above explained feedback weaker, so the setup would be less prone to thermal instabilities and runaways.

So if i uses GP Recyko+ chargable NiMH 1.2V batteries for example in a regular LED flashlight that uses alkaline 1.5V flashlight, i may likely to short the flashlight's LEDs life?
Also, if i using of GP Recyko+ chargable NiMH 1.2V batteries in an alkaline operated laser pointer, i may likely to short the lifetime or even distroy the laser diode of the pointer?
Edit: GP Recyko+ aren't standard NiMH cells, but low self-discharge (LSD) NiMH cells.

So basically the best cells to buy for a LED flashlight are the cheapest Chr@p that you can buy in bulk, as they have such a high internal resistance that they will make the lamps last. Probably the entire box costs as much as a single branded cell.....