When both Organization and FlexOrgs are in use within a tenant, in order to Edit and Delete FlexOrgs a user must belong to a Usergroup. Users that only make use of a role found under Setup -> Admin -> Roles will only be able to Create FlexOrgs but will not be able to Update or Delete them.
To resolve this inability to Edit or Delete FlexOrgs, it's recommended to manually assign the user to the Administrators Usergroup or the corresponding Usergroup for their current role as this will give the user the same level of privileges their Role tied to Organizations gives them within FlexOrgs and allow them to Update and Delete FlexOrgs.