Hi @sudosaurus ,
It seems that you want the Flow to be triggered when Assigned To field has been modified.
Currently, we could not check if the specified filed was modified and then trigger the Flow.
You could consider check the version of the item and get the changes of the specified field. If it was changed, send an email.
Please check this blog and refer to the method to get the version of the specified field:
Check-for-a-Change-in-a-SharePoint-List-Column-Value
Another workaround can be referred to is create a new column as a tag in the list.
When you edit the item, you could set the value of this column, Flow will check the value of the column to determine that if need to trigger Flow.
You could configure trigger conditions, Flow will be triggered when the specified column is equal to the specified value.
For example, I created a tag column, named TriggerOrNot, the type is Yes/No.

Besides, if you don’t want the flow to be triggered when an item is modified, you could use When an item is created as the trigger directly.
Best Regards,