Hey, I cant seem to figure a way to render skybox onto object.
Im currently using reflection shader and it looks like this, but…
but it doesnt look that great. I want it to be seamless - cant see cubes edges.
Does someone has any idea how to do it? 
What exactly do you want to see? Do you want the box to appear to be a window to the skybox? Going by the above image this is for AR. You might want to look into stencils, or a depth writing shader. If you have some control over the shader used to render the AR background you could make sure your “cube” renders first using a Stencil writing shader, and then the AR background is masked by that stencil letting the skybox show through.
Otherwise the next easiest solution is indeed a cubemap of the skybox, but you need a fairly high resolution cubemap for it to work well. You can generate those from script with the RenderToCube() function. A reflection probe is always going to be a little bit blurred since they exist to mimic pbr reflections on rough materials, so it isn’t a great option, though they might still work if you use a shader that explicitly only samples from the top mip of the cubemap using the world view direction rather than “reflection shader” … especially since the one you’re using looks like it’s using a fairly high roughness value or you’re using a very low resolution reflection probe.
The other option is to have an extra camera that renders only the skybox for the current view to a render texture that you then displace on a box using a screen space UV.