If you add a flyback diode you'll minimize the sparking at the contacts of RL1 and perhaps improve its life (depending on the characteristics of the RL2 coil and the RL1 contacts), and you'll reduce the EMI that might be a problem externally, or find its way back through RL1 coil etc. and cause (say) MCU upset.
The down side is that you'll slow the opening of the contacts on RL2 and may reduce its life noticeably. The life of relays is generally specified on the datasheets without the diode.
So, it's a design trade-off and the best choice depends on the details. As well as that binary choice there are other options such as an RC snubber (just a resistor and capacitor in series), a Zener diode + diode or bipolar TVS, a resistor + diode etc.