A texture stamp brush allows you to stamp a single texture anywhere onto an object. Before I begin a basic explanation of how a texture brush works in Blender is required.
A texture brush uses view projection to draw a texture onto an object. The view projects through a circle according to the camera angle and brush position. The important part to note is the circle. Blender doesn't have a square or rectangle brush so every texture you draw will have the edges clipped to fit into the circle. The image below shows a visual representation of the circle brush.
The green area is the texture portion that is drawn. The red area is the clipped area that is not drawn. The drawn area doesn't always go up to the edge of the texture depending on your brush settings. To compensate for this you want to be careful fit your texture within the circle and keep a good distance from the edge of the circle.
For this example I'm going to use the texture below. It's a simple swirl pattern with a transparent background. I chose white so I can adjust the color using the brush settings and get true colors.
For my model I'm using a simple cube with the default UV wrapping. I've already added a material and created a blank texture image of 1024x1024.
To begin select the Texture Paint tab from the work spaces. With the draw brush selected click the Texture Properties tab and select new under the brush drop down.
Under the preview go to image->settings then click open. Select the texture you want to use as a stamp from the browser. You'll see a texture preview after you make your selection.
Select the Active Tool tab. Scroll down to Texture and under mapping select View Plane. This will change the projection type draw a single texture based of the view plane of the brush.
You can stamp the texture by placing the brush over your object and applying a single mouse click. You'll notice the texture fades out at the edges. To correct this you need to change to the brush falloff to none.
In the left window top bar select Falloff. If the bar is cut off you can scroll left or right by placing the mouse over the bar then scrolling the mouse wheel. Under falloff select the icon at the bottom to the far right that looks like a flat bar. The curve will disappear from the chart. The fall off settings tells Blender how far from the edge of the brush to stop drawing. Setting this to zero will draw up to the edge of the circle brush.
Now when you stamp the texture onto the object you will see the full texture with no falloff at the edges. Here is the example I used.