The system mentioned above is not drainage for storm waters rather its the normal guttering system, it can take away only rain water from the streets, that's it!!!
A drainage system with a capacity to drain away such a deadly flood is next to impossible.
The best option can be to make additional canals along the cities or adjacent to the rivers which should connect to a nation wide canal network which will eventually either divert the water to reservoirs, other rivers with low water levels or to the ocean.
In short im talking about a parallel dry river system along with the rivers which would take excess amount of water to the sea.
But making such a network isn't feasible financially.