Why zero flag is not set in INX instruction of microprocessor 8085?

Because that is the way Intel designed the INX instruction of the 8085. The 8080 is also the same. INX increments (and DCX decrements) the 16 bit register pairs or BC, DE or HL, depending on what register pair you specify in the INX (or DCX) instruction. To check is the value is 0 after an INX (or DCX) instruction, you need to OR the values of the register pair into the A register. For example.....

INX H ;increment HL register pair

MOV A,H ; move H register into the accumulator

ORA L ; Logical OR it with the L register

JZ ADDR ; If 0 then jump to ADDR