I'd suggest using a character Style rather than a paragraph Style, as it means you can use this Style in paragraphs that are otherwise formatted differently.
Here's how you can apply it to all Rich Text content controls:
Code:
Sub Demo()
Dim oStyle As Style, oControl As ContentControl
Set oStyle = ActiveDocument.Styles.Add("RTCCStyle", wdStyleTypeCharacter)
With oStyle
.QuickStyle = True
.Font.Underline = wdUnderlineThick
.Font.UnderlineColor = wdColorBlack
.Font.Italic = True
.Font.ColorIndex = wdRed
End With
For Each oControl In ActiveDocument.ContentControls
If oControl.Type = wdContentControlRichText Then
oControl.Range.Style = = oStyle.NameLocal
End If
Next oControl
End Sub
If you only want to apply it to some Rich Text content controls, you'll need additional rules you can test with If statements. For example, any one or more of the Section of the document, the Rich Text content control's title, a bookmarked range could be used.