Hi @nwalaszczyk,
Welcome to the Bunnings Workshop community, it is fantastic to have you with us.
A combination of a mechanical fastener, such as a screw or finish nail, with Liquid Nails, would give you the best hold possible, but if you use a good amount of Liquid Nails, spread out fairly evenly, this would still work, it may just fail quicker than it would if you were to use screws or nails as well.
It is possible to cut a mitre in melamine, but because it chips fairly easily, it can be tough to get a nice, clean cut. To give yourself the best chance of a clean cut, you should use a sharp, fine finish, circular saw blade such as this Diablo 165mm 60T Ultra Finish Circular Saw Blade.
You can also attach some strips of painter's tape over the location of the cut. This will help to anchor the melamine in place, which will help to reduce chip-out from the saw blade.
If you wanted to give this a try, I'd suggest cutting the mitre first so the kickboard is longer than it needs to be. If you are not happy with the result, you can always try again or just cut it square.
If you didn't want to risk it trying to mitre the melamine, you could always run one side of the kickboard past the corner, the equivalent thickness of the melamine and then attach some iron-on melamine to the exposed chipboard, but this would not be as clean a finish.
Let me know what you think and if you have further questions, please don't hesitate to ask.
Jacob
