说明：
1.后台代码添加测试 数据

2.使用 richTextBox.ScrollToVerticalOffset()方法，滚动竖直方向滚动条位置

3.使用定时器DispatcherTimer，修改页面显示数据

4.自己计算处理，已经滚动的高度位置

Xaml代码：

<Grid><Grid.ColumnDefinitions><ColumnDefinition Width="205*"/><ColumnDefinition Width="87*"/></Grid.ColumnDefinitions><Button x:Name="button" Content="开始播放"HorizontalAlignment="Left" Margin="2,36,0,0" VerticalAlignment="Top" Width="75" Grid.Column="1" Height="29" Click="button_Click"/><RichTextBox x:Name="richTextBox" HorizontalAlignment="Left" Height="209" Margin="10,36,0,0" VerticalAlignment="Top" Width="170"></RichTextBox>
</Grid>

后台添加测试数据代码：

public text4()
{InitializeComponent();richTextBox.Document = doc;richTextBox.FontSize = 20;//添加内容appendLine(null, "从你的全世界路过");appendLine("one", "海上生明月");appendLine(null, "从你的全世界路过");appendLine(null, "天涯共此时");appendLine("two", "张三丰");appendLine(null, "从你的全世界路过");appendLine(null, "鲁迅先生");appendLine(null,null);
}
FlowDocument doc = new FlowDocument();
private void appendLine(string name, string line)
{Paragraph p = new Paragraph();if (string.IsNullOrEmpty(name) == false)doc.RegisterName(name, p);Run r = new Run(line);p.TextAlignment = TextAlignment.Center;p.Inlines.Add(r);doc.Blocks.Add(p);
}

定时器显示控制代码：

int pIndex = 0;
double curTop = 0;
private void button_Click(object sender, RoutedEventArgs e)
{//定时控制内容显示和滚动条位置DispatcherTimer _timer = new DispatcherTimer();_timer.Interval = TimeSpan.FromSeconds(1);_timer.Tick += (st, et) =>{//获取指定行的内容BlockCollection col = richTextBox.Document.Blocks;int index = 0;TextElement prev = null;foreach (TextElement item in col){//修改当前行的样式if (index == pIndex){AlterStyle(item, prev);}index++;prev = item;}pIndex++;};_timer.Start();
}
private void AlterStyle(TextElement item, TextElement prev)
{//当前行Paragraph cP = item as Paragraph;cP.Foreground = Brushes.Red;TextRange range = new TextRange(cP.ContentStart, cP.ContentEnd);//滚动位置控制if (pIndex > 0 && range.Text.Length > 0){//上一行，样式回调if (prev != null){prev.Foreground = Brushes.Black;}curTop += range.Text.Length > 7 ? 40 : 20;curTop += 20;richTextBox.ScrollToVerticalOffset(curTop);}
}

运行结果：