Figured it out, was actually rather simple. I'm operating in the Leads object here.
Create a Flow. The flow only needs two elements:
a) a text variable, input only, which is called PB_LeadID
b) a Delete Record action, which has a criteria of Id = PB_LeadID
Create a Process:
a) Insert your criteria (i.e. on Create, if fields are equal to BLAH BLAH BLAH)
b) The action is to launch your flow
c) Once specified, the action will say a variable is required - PB_LeadID. Set this to be LeadID.
Go in, create a record that doesn't meet the criteria. Nothing should happen on save. Create one that DOES meet the criteria, you should be greeted with the Record Is Deleted page when saving.
Why am I doing this?
Web-To-Lead is letting through instances of record creation with key fields missing (I have no idea why, there are mandatory requirements on the field, but hey ho, this is for the web development team to figure out). This is useless information for us, so we just want it killed.