Don't let people sell you flashlights unless they're super cheap and super reliable. :) Especially avoid buying rescue or air defense searchlights - if a product contains the word "rescue" or "defense", its price will cause a jumpscare. Optics isn't a secret art, Wikipedia has all the relevant information - and if you happen to have a solar concentrator with a reasonable focal length, you have a searchlight waiting to happen. :)
Photo taken from 968 meters.
P.S. Just remember: LEDs need to be current-limited and cooled. :)
Is it possible to diy a headlamp? I've always thought it'd be kinda cool and silly to have an obscenely bright flashlight, but I prefer headlamps because it leaves my hands free (and it's automatically pointing at whatever I'm looking at, for better or for worse).
Sure, you can pick from a whole world of different LEDs, and drivers. But there are also a bunch of cheap headlamps that are small and bright.
It sure is possible.
A typical "obscenely bright" LED chip might be Cree XML, but many similar chips exist. You'd need a plano-convex or equivalent Fresnel lens - shorter focal lengths favour compact design. Then you need a driver. Some are fixed while some adjustable with a tiny potentiometer. You'd need an 18650 cell holder (it can be made too, an 18650 will go into a leftover piece of 20 mm electrical cabling pipe with a spring-loaded metal cap engineered of something).
Myself, I bought a nice head lamp, but it broke after one year. The driver board failed. Being of the lazy variety, I replaced the board with a resistor to limit current and now it's been working 3 years already. Not at peak luminosity, the resistor wasn't optimal of course. :)