You do not necessarily need a build a "multitask with interrupts on Arduino". Instead consider using a state machine. First define the problem by drawing a state diagram:
Consider all state you wish to be in. Including your example "...after one card is scanned, 1st relay with the flow sensor has to be turned on and simultaneously the scanning of the second card has to begin...". Once you have defined all states and the rules that need to be tested for before jumping to a new state you can start programming your state machine.
There are plenty of tutorials including this one on the web specifically for people who want to implement a state machine on an Arduino. But, briefly, you will want to create a loop that will execute with out stopping over and over again as fast as possible. This loop will (1) know what the current state is and (2) will repeatedly test to find out if the program can change to any of the possible next states. When you change states is when, if you need to, you perform tasks such at turning the water on or off.