Yes using Power BI REST API to create custom reports is possible but i think only in the latest version of Power BI Desktop.
You can use the feature called power BI Service Live Connection.
To establish a connection to the published report and create your own report based on the published dataset
Follow these steps:
1) Goto Get Data on home page
2) Select Online Service
3) Under Online service, select Power bi Service
Once you're done with your report you can publish it by selecting publish from home in Power BI Desktop.