I think "fling", used here as a verb, refers to the touch screen gesture known as "fling", "flick" or "swipe"; all these seem to refer to the same gesture. Now that touch screens are so widespread (especially with the iPhone, iPad and similar products), a vocabulary has developed for what have become known as "gestures": movements you perform on the screen with one or more fingers to produce certain results.

"Fling" means that you put you finger on the screen and brush or sweep it rapidly in a particular direction, lifting the finger off the screen in the same movement.

Here's a definition of what it does on the iPhone OS; this same document contains entries for other systems too:

"Platform: iPhone OS
Platform Gesture: Flick
Platform Description: A user gesture used to scroll or pan quickly. To flick, users place a finger on the screen and quickly swipe it in the desired direction.
Core Gesture: Fling"
http://www.lukew.com/ff/entry.asp?1071

And here's an illustrated guide (it's called "flick" here):
http://static.lukew.com/TouchGestureGuide.pdf

"Fling (hold and move right/left) the second button on the Home screen until Recipes show up. Click Recipes."
http://www.mightygrocery.com/mighty-grocery-users-guide-sing...

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Note added at 2 hrs (2012-05-11 08:30:28 GMT)
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I suspect that "fling the top toolbar" means you put your finger on the toolbar and perform the "fling" gesture (perhaps downwards), and the buttons and tools appear.

What the fling gesture does in particular cases depends on the system. See the document I cited above: http://www.lukew.com/ff/entry.asp?1071

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Note added at 1 day3 hrs (2012-05-12 09:05:40 GMT)
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Actually it might be better to express this as "brush the surface of the screen". You don't press your finger on the screen at the beginning of the gesture; you normally begin the sweeping or "flinging"/"flicking" movement before touching the screen, so that the finger first makes contact with the screen on the toolbar, in this case.

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Note added at 1 day3 hrs (2012-05-12 09:07:48 GMT)
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In other words, you don't really want to touch the screen and then begin to move your finger; if you do, the initial moment when the finger is stationary on the screen could be interpreted as a "press" gesture, producing an unintended result.