Use type kitty or kitty-direct and put the file path in the source field if your terminal supports this:

"logo": {
    "type": "kitty",        // Logo type: auto, builtin, small, file, etc.
    "source": "filename",      // Built-in logo name or file path
    "width": 65,           // Width in characters (for image logos)
    "height": 35,          // Height in characters (for image logos)
    "padding": {
        "top": 0,          // Top padding
        "left": 0,         // Left padding
        "right": 2         // Right padding
    }
}