Did you find an answer? There are examples of date filters in the documentation here - Filtering and Sorting in the Tableau REST API - Tableau and then - some examples from the JS API although I have not tested with the REST API but here are those links.
The field name and the field value must be exactly as shown in the workbook's underlying data. My recommendation here is to create a field in your data source that makes the calculation: is it the previous month? DATEADD('month',-1,today()) = [YOUR DATE]
And you can use this field in your REST API request.
You can also find more information on filter query views here.
I hope it is helpful.
Did you get it solved?
Asking because im facing same issue.
Can you try the solution I proposed above? Lets me if it is working.
I cannot try your solution, because i don't have access to the view.
I can only read it.
Have any one found out the solution for the relative date ranges in rest api?