Set<Id> permissionSetIds = new Set<Id>();
for (PermissionSetAssignment psa : [SELECT PermissionSetId 
        FROM PermissionSetAssignment 
        WHERE AssigneeId = :currentUser.Id]) {
    permissionSetIds.add(psa.PermissionSetId);
}

Set<Id> accessibleOrgWideAddressIds = new Set<Id>();
for (SetupEntityAccess sea : 
        [SELECT SetupEntityId
        FROM SetupEntityAccess
        WHERE ParentId IN :permissionSetIds
        AND SetupEntityType = 'OrgWideEmailAddress']) {
    accessibleOrgWideAddressIds.add(sea.SetupEntityId);
}

Then query [SELECT Address, DisplayName 
            FROM OrgWideEmailAddress 
            WHERE Id IN :accessibleOrgWideAddressIds)]