Hey there emests!
No, the tiles sadly don't work in HexKit because it doesn't support overlapping tiles. If the map is not all too big, you could just assemble them in an image editing software like Krita (free) or Photoshop. Do you have experience with image editing? As an alternative, we could probably get them to work in Tiled, which is a level editor (my other hex tile sets definitely works in both HexKit and Tiled).
If you need help with Krita or Tiled, you can write me a mail or better, hit me up on Discord (either on my server or directly), and we can figure it out together! :)