You are missing the declaration for AnimateWindow.

Here is your code corrected:

Code:
Public Class Form1

    Public Declare Auto Function AnimateWindow Lib "user32" (ByVal hwnd As IntPtr, ByVal time As Integer, ByVal flags As Integer) As Boolean

    Public Enum AnimateStyles
        Slide = 262144
        Activate = 131072
        Blend = 524288
        Hide = 65536
        Center = 16
        HOR_Positive = 1
        HOR_Negative = 2
        VER_Positive = 4
        VER_Negative = 8
    End Enum

    Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load

    End Sub

    Private Sub Button1_Click(ByVal sender As Object, ByVal e As System.EventArgs) Handles Button1.Click
        AnimateWindow(ChildForm1.Handle, 1000, AnimateStyles.HOR_Negative Or AnimateStyles.Blend)
        ChildForm1.ShowDialog();
    End Sub

End Class