To get the Manager details using SharePoint designer workflow 2013 you will need to use the HTTP Web Service call with REST endpoint URI. Listed below the useful endpoint URI for getting Manager details.
After getting the manager account name in above step, use that to find the email id by again calling a HTTP Service using the below endpoint URL and get the required property from that.
Get all properties of Specific User:
For Office 365/SharePoint Online:
http://siteurl/_api/SP.UserProfiles.PeopleManager/GetPropertiesFor(accountName=@v)?@v=’i:0%23.f|membership|[email protected]’
For SharePoint 2013 On-Premise:
http://siteurl/_api/SP.UserProfiles.PeopleManager/GetPropertiesFor(accountName=@v)?@v=’contoso\mbepari’
Get Specific UserProfile Property of Specific User:
For Office 365/SharePoint Online:
http://siteurl/_api/SP.UserProfiles.PeopleManager/GetUserProfilePropertyFor(accountName=@v,propertyName=’LastName’)?@v=’i:0%23.f|membership|[email protected]’
For SharePoint 2013 On-Premise:
http://siteurl/_api/SP.UserProfiles.PeopleManager/GetUserProfilePropertyFor(accountName=@v,propertyName=’LastName’)?@v=’contoso\mbepari’
Reference: http://spmavericks.com/2014/10/30/sharepoint-designer-2013-workflow-find-manager-alternative/