Yes, the flyback diode is very important on the primary of the coil to make sure the circuit survives. It's connected in the opposite direction of current flow across the primary coils leads, when the 555 turns off the magnetic field in the primary coil collapses and will generate a current, if there's no path for that current to flow through it will generate voltage until the current can flow, which can be lethal to the 555. The diode will be reverse biased when the relay is switched on and when the coils collapsing field generates a reverse voltage it will flow through the diode and dissipate in the coils resistance, preventing high voltages from being generated.