As with almost all of Illustrator, there is a shortcut for this, however, by default it is unassigned. You can assign a shortcut to any specific blending mode-- multiply or screen for example, which can be accessed by a shortcut key. Or alternatively, you can assign a shortcut key to the next and previous blend mode, similar to Photoshop. In Photoshop the keyboard shortcut is Shift + + or - by default, so it might make sense to use a similar keys in Illustrator. By opening up Keyboard Shortcuts in Edit→Keyboard Shortcuts, you can access the menu to change the shortcut keys.