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The usual way is to plot each pairwise result individually. You’ll see this in some publications.
For something more interesting, maybe try the other DE tools such as Limma – you can set one factor level as the contrast to see the effect on the other two conditions (factor levels), all together one set of visualization graphs. Using the control condition as the contrast is one place to start.
You can use the Featurecount result files you have now but should combine them into a matrix. We had another question answered earlier today that has all the links. See → generate a common AnnotateMyID file from two different runs
Hope this helps! 