“…praesagio fuit etiam Domiti patris vox…”
praesagio: neutr. dat. sing. of praesagium, –io. This use of the dative is called the dative of purpose (sometimes called the double dative since it usually takes another dative of the person or thing affected).
A&G (382) write: “The dative of an abstract noun is used to show that for which a thing serves or which is accomplishes.” Examples: rei publicae cladi sunt (they are for a disaster to the state); quibus sunt odio (to whom they are an object of hatred). The verb is usually sum.
Certain usages of the dative of purpose are called predicative datives. The natural English translation is the same for this dative as for a predicative nominative, notes Henry John Roby in a chapter on this phenomenon in his book A Grammar of the Latin Language from Plautus to Suetonius, Volume 2. If we follow that tip, the translation could be as simple as follows:
“… the words of his father Domitius were also a forewarning/presage/portent…”