I tried adding the points as vbnull and also Nothing, and then added the "DontPlot":

UltraChart1.LineChart.NullHandling = Infragistics.UltraChart.Shared.Styles.NullHandling.DontPlot

but when I did that, nothing at all was plotted on the chart.

I solved this issue by taking the point on the map where the 0 value would be plotted, (In my case it is 54. It depends on, of course, the size of the chart), and adding a condition that prevents plots if the Y axis value equals the point where 0 would be plotted. 

Looks perfect now. I'm sure there's a better way but this works for now. I'll eventually collect the plot values from a stored procedure. Here's the final solution..

Public Sub LoadChart()
        Dim dt As New DataTable
        Dim tnull As Int32 = Nothing

        dt.Columns.Add("Series Labels", GetType(String))

        dt.Columns.Add("PPW Submitted", GetType(Integer))
        dt.Columns.Add("Responsible Person Approved", GetType(Integer))
        dt.Columns.Add("OIM Approved", GetType(Integer))
        dt.Columns.Add("PTW Admin Activated", GetType(Integer))
        dt.Columns.Add("De-Activated (Responsible Person)", GetType(Integer))
        dt.Columns.Add("Closed (OIM)", GetType(Integer))

        'Add the rows of data
        dt.Rows.Add(New [Object]() {"Workflow", 10, 10, 10, 0, 0, 0})

        UltraChart1.ChartType = ChartType.LineChart
        UltraChart1.Axis.X.Labels.Orientation = TextOrientation.Horizontal
        UltraChart1.Axis.X.Labels.ItemFormat = Infragistics.UltraChart.Shared.Styles.AxisItemLabelFormat.ItemLabel
        UltraChart1.Axis.Y.Labels.Visible = False

        Me.UltraChart1.DataSource = dt
        Me.UltraChart1.DataBind()
    End Sub

Private Sub Chart_FillSceneGraph(ByVal sender As Object, ByVal e As Infragistics.UltraChart.Shared.Events.FillSceneGraphEventArgs) _
        Handles UltraChart1.FillSceneGraph

        Dim i As Int32 = 0
        Dim dataPointColour As System.Drawing.Color
        Dim symbol As Infragistics.UltraChart.Core.Primitives.Symbol
        Dim symbols As New Infragistics.UltraChart.Core.Primitives.PrimitiveCollection

        For Each p As Infragistics.UltraChart.Core.Primitives.Primitive In e.SceneGraph
            Dim polyline As Infragistics.UltraChart.Core.Primitives.Polyline

            If (TypeOf p Is Infragistics.UltraChart.Core.Primitives.Polyline) Then
                polyline = CType(p, Infragistics.UltraChart.Core.Primitives.Polyline)
            Else
                polyline = Nothing
            End If

            If polyline IsNot Nothing Then
                dataPointColour = polyline.PE.Fill
                polyline.PE.Fill = Color.Transparent

                For Each dataPoint As Infragistics.UltraChart.Core.Primitives.DataPoint In polyline.points
                    symbol = New Infragistics.UltraChart.Core.Primitives.Symbol()
                    If Convert.ToInt32(polyline.points(i).point.Y) <> 54 Then
                        symbol.icon = Infragistics.UltraChart.Shared.Styles.SymbolIcon.Circle
                        symbol.iconSize = Infragistics.UltraChart.Shared.Styles.SymbolIconSize.Large
                        symbol.PE.Fill = dataPointColour
                        symbol.point = dataPoint.point
                        symbols.Add(symbol)
                    End If

                    i += 1
                Next
            End If
        Next

        e.SceneGraph.AddRange(symbols.ToArray())
    End Sub

Here's a pic of the final chart.