Apple - iOS 8.4 Apple Music App: How to shuffle all songs by an artist?
Instead of selecting the artist to display the albums and songs of the artist, tap the image of the artist and the artists songs will play shuffled.
Answer: Siri > Play " artist " songs shuffle
These seem to be the current ways to shuffle in the new 8.4 Music.app: About.com "How to Shuffle Music on the iPhone" - Updated 7/8/2015
Shuffle All Songs
To shuffle all the songs in your Music app library, which will give you the greatest variety and a roughly random order of songs, follow these easy steps:
Open the Music app
Tap My Music
Make sure the menu just below Apple Music is set to Songs
Find a song you'd like to listen to and tap it to begin it playing
Tap the playback bar just above the buttons at the bottom of the screen to reveal the album art and full set of Music app controls
At the bottom of the screen, tap the Shuffle button, which is two arrows crossing over each other. You'll know it's enabled when it's highlighted.
With that done, your next song will be randomly chosen and you're off on a shuffling adventure. Use the forward arrow to skip to the next song or the back arrow to return to the last one.
To turn off shuffle, just tap the two-arrow icon again so it is no longer highlighted.