Hi @Anonymous,
Could you please share a screenshot of your flow's configuration?
Do you use the "Add new StaffHub shifts to your Office 365 calendar" built-in template to create your flow?
I suppose that you use the "Add new StaffHub shifts to your Office 365 calendar" built-in template to create your flow, is it true? If you want to delete the corresponding shift (Outlook event) from your Outlook calendar, you should include the Shift ID within your Outlook event. When a shift is deleted from your StaffHub, you could find the specific the Outlook event based on the Shift ID and then delete it.
I have made a test on my side and please take a try with the following workaround:
Move StaffHub Shifts to Outlook calendar (use the "Add new StaffHub shifts to your Office 365 calendar" built-in template to create my flow😞

Within Body field of the "Create event (V2)" action, type the Shift ID dynamic content of the "Get Shift" action.
The flow works successfully as below:

When a Shift is deleted in your StaffHub, remove event from your Office 365 Outlook calendar:
- Add a "When a shift is deleted in a team" trigger, specify Team Id.
- Add a "Get events (V2)" action, specify Calendar id.
- Add a "Apply to each" action, input parameter set to output of "Get events (V2)" action.
- Within "Apply to each" action, add a "HTML to text" action, Content field set to Body dynamic content of the "Get events (V2)" action.
Add a Condition, left input box set to output of "HTML to text" action, right input box set to Resource Id dynamic content of the trigger, within middle drop down, choose contains. Within "If/yes" branch of Condition, add a "Delete event" action, specify Calendar id, Id field set to Id dynamic content of the "Get events (V2)" action.
Image reference:
The flow works successfully as below:
Best regards,
Kris