All the api functions approach from the workflow aspect to show the hierarchy and the workflow attributes. And the Entity is an attribute of the workflow. The options you have are to use the existing api calls such as BRApi.Workflow.Metadata.GetProfileEntities or query the WorkflowProfileEntities table something like this:
SELECT WPH.ProfileName
FROM WorkflowProfileEntities AS WPE INNER JOIN
Member AS M ON WPE.EntityMemberID = M.MemberId INNER JOI
WorkflowProfileHierarchy AS WPH ON WPE.WorkflowProfileKey = WPH.ProfileKey
WHERE (M.DimTypeId = 0) AND (M.Name = 'myentity')