It is now possible to manage SharePoint permissions in Microsoft Flow with the help of Plumsail SharePoint (Third-party connector), which is a part of Plumsail Actions product with a fair price.
There is an action, called Change Permissions that gives you the ability to:
- Grant Permissions on Site
- Remove Permissions from Site
- Remove All Permissions from Site
- Restore Permissions Inheritance for Site
- Grant Permissions on List
- Remove Permissions from List
- Remove All Permissions from List
- Restore Permissions Inheritance for List
- Grant Permissions on Item
- Remove Permissions from Item
- Remove All Permissions from Item
- Restore Permissions Inheritance for Item
Here are a couple of examples of Flows:
Set item level permissions (break role inheritance and assign permissions)
Create site by custom template and grant permissions
Regarding the limitations of Microsoft Flow. SharePoint Designer functionality is almost covered in Microsoft Flow. There are still some issues with reading and writing multichoice fields, lookups, and metadata columns. But Microsoft team claims to fix it soon.
SharePoint Designer workflows can be started under App step permissions. Microsoft Flow is always started by a user who specified credentials in SharePoint connector.
SharePoint Designer workflow can be edited by any user with appropriate permissions on a SharePoint site. Microsoft Flow has Team Flows instead. That allows a few users to collaborate on the same Flow.
Note: I'm a part of Plumsail Actions development team