You would need macros to do this via buttons since they aren't built-in. You can do a series of macros to toggle the colours. There is a finite number of highlight colours but if you know the available constant names for the colours then you just build another macro for each one.
Code:
Sub HL1()
SetHiLite wdYellow
End Sub
Sub HL2()
SetHiLite wdBrightGreen
End Sub
Function SetHiLite(iCol As Long)
If Selection.Range.HighlightColorIndex = iCol Then
Selection.Range.HighlightColorIndex = wdNoHighlight
Else
Selection.Range.HighlightColorIndex = iCol
End If
End Function