This is an interesting question, and the answer depends on what part of the Roman Empire we're talking about. We might hypothesize that kilns required a great deal of wood or charcoal fuel, and that deforestation occurred as a result. However, that wasn't always the case. Take Egypt, for example: they have very little in the way of wood resources, yet they managed to be one of the top producers of amphorae. How could a semi-desert area have sufficient fuel to maintain significant pottery production? They probably used agricultural and handicraft waste instead of wood or charcoal. Egyptian papyri have been discovered which point to the use of chaff as fuel (see p. 171 of "Amphora Production in the Roman World" by Scott Galimore in the Bulletin of the American Society of Papyrologists). However, we can assume that in more heavily wooded areas, wood and charcoal were a more important source of fuel for pottery making.

Deforestation in the ancient world was a huge issue, and was remarked upon by several ancient authors, including Pliny, Theophrastus, Strabo, Vergil, Dionysus of Halicarnassus, and Varro. In their passing remarks, these ancient voices paint a fragmentary picture of severe and progressive deforestation throughout the Mediterranean. Donald J. Hughes' article "Deforestation, Erosion, and Forest Management in Ancient Greece and Rome" in the Journal of Forest History is a good place to read about this. Hughes says that "Early writers may call an area forested that later writers know as barren, while traces of vanished forests persist in place names like Elatea ('Firtown'), Pityoussa ('Pineville'), Castanea ('Chestnugburg'), or Xylopolis ('Timber City')." Amphora production certainly contributed to deforestation, but it was not necessarily the most important factor in the denuding of ancient forests. Wood was used for everything, from building to crafts to fuel for all kinds of activities. In fact, the words for 'wood' (materia in Latin and hyla in Ancient Greek) came to mean merely 'substance' or 'stuff,' it was that ubiquitous. But circling back to your question, it's impossible to determine what share of the deforestation was due to amphora production.