LTspice’s educational examples folder includes NE555.asc, which is a full transistor-level model of the 555 timer.
I removed the external components that allow this example to simulate, and saved out the netlist of just the internal 555 structure into a subcircuit library:
NE555.lib (1.2 KB)
You can use this LIB file within KiCad. I had no idea what you were trying to do with your original circuit in the PDF, so I just built a simple astable circuit and successfully simulated that. I attached a ZIP of this example project.
NE555_test.zip (5.1 KB)