Can I safely plug a 15amp socket to 13amp socket, through multiple adapters?
Do not do this. 


First of all even you would have to admit that the assemblage would be unwieldy at best. 
Secondly having so many connections in series increases the overall resistance of the circuit and leads to a voltage drop and increase in temperature.
Kludges like what you propose often lead to unfortunate results. 


Get a true sense of danger and respect for high powered live mains connections  and live to tell your grandchildren about how to live a safe life.