The wording of the English translation seemed odd to my modern ear (Whiston published his translation in 1737 CE or so), so I looked closer.
JOE Wars of the Jews 4:81
nor did anyone escape [Gamala] except two women (διεσώθη δὲ πλὴν δύο γυναικῶν οὐδείς),
who were the daughters of Philip (τῆς Φιλίππου δὲ ἦσαν ἀδελφῆς θυγατέρες αὗται)
and Philip himself was the son of a certain eminent man called Jacimus, (αὐτὸς δὲ ὁ Φίλιππος Ἰακίμου τινὸς ἀνδρὸς ἐπισήμου)
who had been general of King Agrippa's army; (τετραρχήσαντος Ἀγρίππᾳ τῷ βασιλεῖ)
When Josephus says "τῆς Φιλίππου δὲ ἦσαν ἀδελφῆς θυγατέρες αὗται" the name "Philip" is used as if we should know who Philip was.
Ahh, there he is, in War 2:
Wars of the Jews 2:556 After this calamity had befallen Cestius, many of the most eminent of the Jews fled from the city [Jerusalem], as from a ship when it was going to sink; Costobarus, therefore, and Saul, who were brothers, together with Philip, the son of Jacimus, who was the commander [στρατηγῷ] of King Agrippa's forces, [he (Jacimus?) was part of an expeditionary force sent by Philip the Tetrarch,* ran away from the city, and went to Cestius.
*Wars of the Jews 2:421 But Agrippa was equally solicitous for those who were revolting, and for those against whom the war was to be made, and was desirous to preserve the Jews for the Romans, and the temple and metropolis for the Jews; he was also sensible that it was not for his own advantage that the disturbances should proceed; so he sent [as an expeditionary force] three thousand horsemen to the assistance of the people [of Jerusalem who were not part of the revolt], out of Auranitis, and Batanea, and Trachonitis, and these under Darius, the master of his cavalry, and Philip, the son of Jacimus, the general of his army [στρατηγῷ δὲ τῷ Ἰακίμου Φιλίππῳ].
JOE Life of Flavius Josephus 1:46 But Gamala persevered in its allegiance to the Romans, for the reason following: Philip, the son of Jacimus, who was their governor under king Agrippa, had been unexpectedly preserved when the royal palace at Jerusalem had been besieged [in the initial stages of the revolt]; but, as he fled away, had fallen into another danger; and that was, of being killed by Manahem, and the robbers that were with him;
47 but certain Babylonians, who were of his kindred, and were then in Jerusalem, hindered the robbers from executing their design. So Philip stayed there four days, and fled away on the fifth, having disguised himself with fictitious hair, that he might not be discovered; and when he was come to one of the villages to him belonging, but one that was located at the borders of the citadel of Gamala, he sent to some of those who were under him, and commanded them to come to him;
48 but God himself hindered that his intention, and this for his own advantage also; for had it not so happened, he had certainly perished; for a fever having seized upon him immediately, he wrote to Agrippa and Bernice, and gave them to one of his freedmen to carry them to Varus
49 who at this time was procurator of the kingdom, which the king and his sister had intrusted him withal, while they were gone to Berytus with an intention of meeting Gessius.
50 When Varus had received these letters of Philip, and had learned that he was preserved, he was very uneasy at it, as supposing that he should appear useless to the king and his sister, now Philip was come. He therefore produced the carrier of the letters before the multitude, and accused him of forging the same; and said that he spoke falsely when he related that Philip was at Jerusalem, fighting among the Jews against the Romans. So he slew him.
51 And when this freedman of Philip did not return again, Philip was doubtful what should be the occasion of his stay, and sent a second messenger with letters, that he might, upon his return, inform him what had befallen the other that had been sent before, and why he tarried so long.
52 Varus accused this messenger also, when he came, of telling a falsehood, and slew him; for he was puffed up by the Syrians that were at Caesarea [Philippi], and had great expectations; for they said that Agrippa would be slain by the Romans for the crimes which the Jews had committed, and that he should himself take the government, as derived from their kings; for Varus was, by the confession of all, of the royal family, as being a descendant of Sohemus, who had enjoyed a tetrarchy about Libanus;
53 for which reason it was that he was puffed up, and kept the letters to himself. He contrived, also, that the king should not meet with those writings, by guarding all the passes, lest anyone should escape, and inform the king what had been done. He moreover slew many of the Jews, in order to gratify the Syrians of Caesarea [Philippi].
54 He had a mind also to join with the Trachonites in Batanea, and to take up arms and make an assault upon the Babylonian Jews that were at Ecbatana; for that was the name they went by.
Life 1:179 But before this, it happened that Philip, the son of Jacimus, went out of the citadel of Gamala [where he had holed up in the town's citadel in hopes of preserving the city and inhabitants for the Romans] upon the following occasion:
180 when Philip had been informed that Varus [king Philip's former head of state] was put out of his government by King Agrippa, and that Equiculus Modius, a man that was of old his friend and companion, was come to succeed him, he wrote to him and related what turns of fortune he had had, and desired him to forward the letters he sent to the king and queen.
181 Now, when Modius had received these letters, he was exceedingly glad, and sent the letters to the king and queen, who were then about Berytus.
182 But when King Agrippa knew that the story about Philip was false, (for it had been given out, that the Jews had begun a war with the Romans, and that this Philip had been their commander in that war,) he sent some horsemen to conduct Philip to him;
183 and when he was come, he greeted him very obligingly, and showed him to the Roman commanders, and told them that this was the man of whom the report had gone about as if he had revolted from the Romans.
184 He also bade him to take some horsemen with him, and to go quickly to the citadel of Gamala, and to bring out there all his domestics, and to restore the Babylonians to Batanea again. He also gave it him in charge to take all possible care that none of his subjects should be guilty of making any sedition. Accordingly, upon these directions from the king, he made haste to do what he was commanded.
The whole story of this Philip son of Jacimus seems to be this: I think that Philip, son of Jacimus (who had been the chief army commander under Philip), sent to help quell the uprising in the very beginning, was forced to flee tetrarch Philip's palace in Jerusalem. Philip son of Jacimus' escaped to Gamala and is let into the citadel by friends. But Varus, the procurator under Philip the tetrarch, was acting against Philip's orders, killing the ambassadors sent by Philip the son of Jacimus. Varus was ousting Judeans and Mesopotamians (probably also Judeans) from cities in Philip's kingdom, effectively attempting to set himself up as a king, as he was of royal blood, a descendant of Sohemus, who had enjoyed a tetrarchy about Libanus. Philip the tetrarch, when he found out, had Varus is removed from his post. Philip son of Jacimus is reinforced with troops from the new procurator. However, Philip eventually goes on to loose control of the townGamala. Not sure if Philip the son of Jacimus managed to live through the events that led to the Romans overrunning Gamala, although his two daughters were still there. Many of these towns alternated between the control of several factions in the rebellion. Just the same, even Josephus' wife and family were still in Jerusalem when the Romans overran the city, and they too escaped death by the enraged soldiers, and likely also in deep hiding places.
I don't think this has anything to do with the Philip in early Christian lore.