RTF is pure text, so it can be saved like any other text content with a TextOutputStream.
https://documentation.xojo.com/api/files/textoutputstream.html#textoutputstream
This slightly modified example writes the Textarea1 styled text RTF Data into a file.
Var f As FolderItem
Var t As TextOutputStream
f = FolderItem.ShowOpenFileDialog(FileTypes1.RTF)
If f <> Nil Then
t = TextOutputStream.Open(f)
t.Write(TextField1.StyledText.rtfdata)
t.Close
End If