I want to make a handmade LED-flash for my project. I need to know an angle size of a beam from typical flashlight. Let's say from Samsung WB50F for example. It's a Xenon one, but what is the angle of its beam? I can't find online an answer.
An on-camera flash has to cover at least the area seen by the camera objective. The more expensive ones can adjust the covered angle (either automatically or manually), and the angle is expresses in mm focal length, on a full-frame camera.
The example you give (Samsung WB50F) is a camera, with a 24-300 mm zoom (FF equivalent). Looking up 24mm lenses tells us they cover an angle of 84° (over the image diagonal). That means that for on-camera use, your flash has to cover at least that angle if you don't want dark corners (vignetting).
If you plan to use the flash off-camera, you'll have to take into account the distance between flash and object: if you move the flash closer, you'll need a wider beam, farther away, and you can use a narrower beam.
But keep in mind that a wide beam will be less efficient than a narrow beam: it will deliver less light per m² of your subject area, so the narrowest beam you can use is the most efficient (which is why some flashes allow adjustment of the beam).