If a customer cancels an order in Pressero, how can we also cancel the order in tFLOW?

The sync process between Pressero and tFLOW is mostly one way: From tFLOW to Pressero.
The only exception of course is when the order is placed and syncs the order to tFLOW along with the artwork. After that event, all the remaining updates are one-sided, coming from tFLOW to Pressero only.
 
This means if you update the status in Pressero, it will not update the status in tFLOW. 
But updating the status in tFLOW does update the status in Pressero. Therefore the correct way to cancel an order when you have Pressero and tFLOW integrated is to make the cancellation in tFLOW, which will then update Pressero.
 
 
 
If you do not see the "Cancel" option in the menu, be sure that the Role your account is assigned includes the permission to Cancel Orders.
If you are not sure what Role your account is assigned: 
  1. Go to the gears icon on the upper right and click on Users.
  2. Find your user, and scroll down until you see the Role field and take note of which role is assigned.
  3. Next, return to the gears icon on the upper right and click on Roles, then search for the role. Once you find it, open it and click on the Permissions tab.
  4. Don't forget to Save your changes.
 
 
 
If you take a look at the workflow diagram below (based on 1 step approval workflow. More on workflows here.), you can see where all the sync events happen.
You can see that certain things "trigger" status changes automatically, such as when a proof is approved or rejected, or when a job is cancelled altogether.
 
So the proper way to "Cancel" a Pressero order when you have a tFLOW integration is to cancel the order from tFLOW.
But once a tFLOW job reaches a "Sent to Production" status, that's the end of the line for tFLOW updates to Pressero.
If you must cancel a job that late in the process, then you're safe to cancel it from Pressero only - only if the status in Pressero is "Sent to Production" or later.