You can use the ArcSDESQLExecute function to execute the below SQL query to find the privileges for each user:
select permission_name, pr.name
from sys.database_permissions pe
join sys.database_principals pr on pe.grantee_principal_id = pr.principal_id
where pe.class = 1
and pe.major_id = object_id('<owner>.<feature class name')
and pe.minor_id = 0;
You will want to replace '<owner>.<feature class name>'.
Here is an example:
import arcpy
sde_conn = arcpy.ArcSDESQLExecute(r"Database Connections\DBO@SQLSERVER.sde")
sql_statement = "select permission_name, pr.name from sys.database_permissions pe join sys.database_principals pr on pe.grantee_principal_id = pr.principal_id where pe.class = 1 and pe.major_id = object_id('vector.AIRPORTS') and pe.minor_id = 0;"
sde_return = sde_conn.execute(sql_statement)
for row in sde_return:
print "User: " + row[1] + "\t Privilege: " + row[0]