In the new Microsoft Azure portal, when you create a new Web App, you might struggle to find your FTP user credentials. This is how you can find them.
1) Open portal.azure.com and browse to the Web App you want to access to.
2) Click on the "Get Publish..." button as per screenshot below. It will download an XML file.
3) Open that file with a text editor and you will find the publishUrl, userName and userPWD fields you need.