我认为段落抓取任何触摸事件。我没有任何触摸设备进行测试。但我无法在文档内使用鼠标滚动FlowDocumentScrollViewer。
一个可能的解决方案是处理预览事件，并根据移动的delta滚动相关的scrollviewer。
这里的处理程序同时处理鼠标和触摸。

bool IsScrolling = false; 
    Point LastPoint;
    private void FlowDocumentScrollViewer_PreviewMouseDown(object sender, MouseButtonEventArgs e)
    {
        HandleDown(sender);
    }

    private void HandleDown(object sender)
    {
        var sv = sender as FlowDocumentScrollViewer;
        if (sender != null)
        {
            IsScrolling = true;
            LastPoint = Mouse.GetPosition(sv);
        }
    }

    private void FlowDocumentScrollViewer_PreviewMouseMove(object sender, MouseEventArgs e)
    {
        HandleMove(sender);
    }

    private void FlowDocumentScrollViewer_PreviewMouseUp(object sender, MouseButtonEventArgs e)
    {
        IsScrolling = false;
    }

    private void FlowDocumentScrollViewer_PreviewTouchDown(object sender, TouchEventArgs e)
    {
        HandleDown(sender);
    }

    private void FlowDocumentScrollViewer_PreviewTouchUp(object sender, TouchEventArgs e)
    {
        IsScrolling = false;
    }

    private void FlowDocumentScrollViewer_PreviewTouchMove(object sender, TouchEventArgs e)
    {
        HandleMove(sender);
    }

    private void HandleMove(object sender)
    {
        var fdsv = sender as FlowDocumentScrollViewer;
        if (fdsv == null || !IsScrolling)
        {
            return;
        }
        var ThisPoint = Mouse.GetPosition(fdsv);
        double dY = (ThisPoint.Y - LastPoint.Y);
        double dX = (ThisPoint.X - LastPoint.X);

        ScrollViewer sv = fdsv.GetChildOfType<ScrollViewer>();
        sv.ScrollToVerticalOffset(sv.VerticalOffset - dY);
        LastPoint = ThisPoint;
    }

在FlowDocumentScrollViewer上处理这些事件

<FlowDocumentScrollViewer Height="350" 
                              IsSelectionEnabled="False" 
                              ScrollViewer.PanningMode="Both"
                              PreviewMouseDown ="FlowDocumentScrollViewer_PreviewMouseDown"
                              PreviewTouchDown="FlowDocumentScrollViewer_PreviewTouchDown"
                              PreviewMouseUp="FlowDocumentScrollViewer_PreviewMouseUp"
                              PreviewTouchUp="FlowDocumentScrollViewer_PreviewTouchUp"
                              PreviewMouseMove="FlowDocumentScrollViewer_PreviewMouseMove"
                              PreviewTouchMove="FlowDocumentScrollViewer_PreviewTouchMove"
                              >

有了这些地方，我可以拖动和滚动鼠标。
获取子类型

public static class ExtensionMethods
{
    public static T GetChildOfType<T>(this DependencyObject depObj) where T : DependencyObject
    {
        if (depObj == null) return null;

        for (int i = 0; i < VisualTreeHelper.GetChildrenCount(depObj); i++)
        {
            var child = VisualTreeHelper.GetChild(depObj, i);

            var result = (child as T) ?? GetChildOfType<T>(child);
            if (result != null) return result;
        }
        return null;
    }
}