You can save RichEditBox content as RTF file.
XAML
<Grid Background="{StaticResource ApplicationPageBackgroundThemeBrush}">
<StackPanel Margin="200">
<RichEditBox x:Name="REB" Height="300" Width="400" />
<Button Content="Save as RTF" Click="btnSaveAsRtf_Click" HorizontalAlignment="Center" Margin="0,20,0,0"/>
</StackPanel>
</Grid>
C#
private async void btnSaveAsRtf_Click(object sender, RoutedEventArgs e)
{
var RtfFile = await ApplicationData.Current.TemporaryFolder.CreateFileAsync("RtfFile.rtf", CreationCollisionOption.GenerateUniqueName);
using (var stream = await RtfFile.OpenAsync(FileAccessMode.ReadWrite))
{
REB.Document.SaveToStream(TextGetOptions.FormatRtf, stream);
}
}