Ok I have a ViewFlipper with three LinearLayouts nested inside it. It defaults to showing the first one. This code:
// Assumptions in my Activity class:
// oldTouchValue is a float
// vf is my view flipper
@Override
public boolean onTouchEvent(MotionEvent touchEvent) {
  switch (touchEvent.getAction()) {
    case MotionEvent.ACTION_DOWN: {
      oldTouchValue = touchEvent.getX();
      break;
    }
    case MotionEvent.ACTION_UP: {
      float currentX = touchEvent.getX();
      if (oldTouchValue < currentX) {
        vf.setInAnimation(AnimationHelper.inFromLeftAnimation());
        vf.setOutAnimation(AnimationHelper.outToRightAnimation());
        vf.showNext();
      }
      if (oldTouchValue > currentX) {
        vf.setInAnimation(AnimationHelper.inFromRightAnimation());
        vf.setOutAnimation(AnimationHelper.outToLeftAnimation());
        vf.showPrevious();
      }
      break;
    }
    case MotionEvent.ACTION_MOVE: {
      // TODO: Some code to make the ViewFlipper
      // act like the home screen.
      break;
    }
  }
  return false;
}
public static class AnimationHelper {
  public static Animation inFromRightAnimation() {
    Animation inFromRight = new TranslateAnimation(
    Animation.RELATIVE_TO_PARENT, +1.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f);
    inFromRight.setDuration(350);
    inFromRight.setInterpolator(new AccelerateInterpolator());
    return inFromRight;
  }
  public static Animation outToLeftAnimation() {
    Animation outtoLeft = new TranslateAnimation(
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, -1.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f);
    outtoLeft.setDuration(350);
    outtoLeft.setInterpolator(new AccelerateInterpolator());
    return outtoLeft;
  }
  // for the next movement
  public static Animation inFromLeftAnimation() {
    Animation inFromLeft = new TranslateAnimation(
    Animation.RELATIVE_TO_PARENT, -1.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f);
    inFromLeft.setDuration(350);
    inFromLeft.setInterpolator(new AccelerateInterpolator());
    return inFromLeft;
  }
  public static Animation outToRightAnimation() {
    Animation outtoRight = new TranslateAnimation(
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, +1.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f,
    Animation.RELATIVE_TO_PARENT, 0.0f);
    outtoRight.setDuration(350);
    outtoRight.setInterpolator(new AccelerateInterpolator());
    return outtoRight;
  }
}
... handles the view flipping but the animations are very "on/off". I'm wondering if someone can help me out with the last part. Assuming that I can access the LinearLayouts, is there a way where I can set the position of the layouts based on deltaX and deltaY?
Someone gave me this link and said I should refer to the applyTransformation method for hints on how to do this but I don't know how to repeat this same behavior.
Moving the view while you're moving your finger is easily done:
case MotionEvent.ACTION_MOVE:
    final View currentView = vf.getCurrentView();
    currentView.layout((int)(touchEvent.getX() - oldTouchValue), 
            currentView.getTop(), currentView.getRight(), 
            currentView.getBottom());
break;
Now this only moves the current view, not the neighbors. I didn't test that yet, but those can probably be obtained by getChildAt:
vf.getChildAt(vf.getDisplayedChild() - 1); // previous
vf.getChildAt(vf.getDisplayedChild() + 1); // next
Hope that helps.
If I understand your request, this effect should now be implemented using a View Pager
Looks like this:

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