Just as the title says. Or should it really be "Asclepiadae", since it comes from "Asclepius"?
The word that you are asking about was derived by adding (the plural form of) a patronymic suffix to a Greek name with unknown ultimate etymology. The a in the second-to-last syllable of patronymics ending in "adae" (including those ending in "iadae") is short as a rule.* The e before the "p" here is long, since the Greek source word is spelled with η. I don't know whether there is any certain way of determining the length of the first "a", or of the "i", but I would guess that both are short, based on my intuitions about the distribution of long and short "a" and "i" in Greek.
The Wikipedia entry on Asclepius contains a quotation from Beekes that makes the following comments on variant forms of the name:
The name is typical for Pre-Greek words; apart from minor variations (β for π, αλ(α) for λα) we find α/αι (a well known variation; Fur. 335–339) followed by -γλαπ- or -σκλαπ-/-σχλαπ/β-, i.e. a voiced velar (without -σ-) or a voiceless velar (or an aspirated one: we know that there was no distinction between the three in the substr. language) with a -σ-.
That article also gives "Aesculapius" as a Latin version of the name. Based on this information, I am pretty puzzled by the absence of "s" in the form that you give, but I don't know enough to say anything definite about whether it is a mistake.
The LSJ Greek dictionary has an entry for Ἀσκληπιάδαι, defined as "a name for physicians". "Asclepiadae", which is simply the regular latinization of "Ἀσκληπιάδαι", certainly seems to be a valid and used form in Latin. If you Google it, you will see a bunch of examples. It would be expected to be pronounced the way it is spelled: i.e., reconstructed Classical Latin pronunciation would be something like [askleːˈpiadae̯], "Ecclesiastical" pronunciation would be something like [asklɛˈpiadɛ], "Traditional English pronunciation" would be /ˌæsklɪˈpaɪədiː/, English anglicized "restored pronunciation" would be something like /ˌɑːskleɪˈpiːədaɪ/.
*Grammar of the Latin Language, 64th Ed., Andrews and Stoddard, 1858; §100, p. 49