The steps are these:

1) Get the specific compliance view which gives you a result containing the name, baseViewName and policyQueries using the endpoint: <UCMDB_Server>/rest-api/policy/complianceView/ViewName
2) Next run the compliance view and get a result back using the endpoint: <UCMDB_Server>/rest-api//policy/calculate?chunckSize=300
This will give a result like this:
{
 "viewResultId" : eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJ1bmlxdWVfc2FsdCI6ImE4ZGZiNjAyLTRjNmItNDJhOC04YzdiLTdlMzBhNmRjNDM1MSIsInRpbWVzdGFtcF9zYWx0IjoxNjU1NDA4MTU5NTUxLCJ1c2VybmFtZSI6ImFkbWluOjE6VUNNREIifQ.Js7iFbI-pD84zq5VejzxnP28I6jSXlHWVKJemXpZS2M"
}

3) Next, calculate what is in the view execution passing a body for compliant like this:
{
'path':
[
{
'pathElementId': 'COMPLIANT',
'pathElementType': 'COMPLIANT'
}
],
'viewExecutionId': '<ID>'
}

using the method: <UCMDB_Server>/rest-api/uiserver/modeling/views/result/numberOfElementsForPath

FYI, if you ever want to make sure you understand the calls and the payload, use the developer tools in chrome (or IE/Firefox)... to see the calls as you calculate this in the CMS UI.

Not all REST API calls are exposed in SaaS, which may further compound the issue.  I can send you my rest.py example script which contains all the code to run a compliance view if you like, but it is too large to post here.

Keith