I do agree with the relays should be in parallel.
Note that the original circuit was contributed by theislander261 (John) and specified the use of opto isolated relays for additional protection (he used an opto22 module) Note point 4 in the primer.
Code:
Both sides of the circuit needs to be isolated by opto-isolated relays until probing is being undertaken
Using Opto isolated relays is to provide an additional level of protection as if something goes wrong the torch voltage could jump mechanical relay contacts...
Whilst the temptation is to use a single dual channel relay, this does not provide a significant level of protection in our view. ( I can say our view as the primer includes input from a number of users).
So if Opto isolated relays are used, there is no need for flyback diodes.
For your own safety, I would recommend that you replace you relay with opto isolated ones. (I am assuming you are using a mechanical relay as you have suggested the use of flyback diodes)
Of course an updated diagram via a pull request would be welcome!