I haven't read Miles' book yet, but the main difficulty here is the absolute lack of any Carthaginian sources. There is, however, a passage from the Silius Italicus' Punica wherein Silius claims that Hamilcar "reckoned his long descent from Belus".

In the traditional story of Carthage's founding, Dido (also known as Elissa) fled her brother Pygmalion the King of Tyre sometime after he arranged the murder of her husband Acerbas, the high priest of Melqart. Now, in Tyre (and Canaanite religion generally) the priesthood was hereditary. Additionally, the king (and presumably the royal family, by extension) had religious duties as well, but rather to the goddess Astarte. If we accept Silius Italicus' account of Hamilcar's descent from Elissa, then it should follow that one or the other or potentially two priesthoods ought to have remained within the Barca dynasty down to Hannibal's own time.

While in Tyre and the Canaanite religion the monarch was seen as the physical embodiment of the divine, Carthage had greatly reduced the power of the monarchy by the after ca.480BCE and done away with it altogether around 308BCE. Though Aristotle, in his Politics, calls the Carthaginian rulers 'kings', a more accurate term might be 'judges', per the related Hebrew word (Punic 'sufet'/'suffete'; Hebrew 'shofet'/'shophet').

Furthermore, also during the 5th century BCE, Carthage appears to have reduced ties to her mother-city of Tyre (potentially instigated by the disastrous Battle of Himera in 480BCE). This century also marks the supersession of Astarte and Melqart in Carthage by Tanit (or Tinnit) and Ba'al Hammon, respectively. This break from the chief deities of Tyre, as well as Carthage's eschewal of their own monarchy, suggest that Hannibal would not have been considered divine.

Hannibal's piety is well-attested, but there's nothing to substantiate a claim that he was an incarnation of Melqart (nor do I personally think Hannibal's character seems the type to put forth such a claim--he was no Caesar). If he was accepted as descended from Herakles-Melqart, it would have been in much the same way that many of the noble families of Classical Greece traced their lineage to heroes found in Homer's Iliad.

I hope I was able to shed some light on your question. I know one is supposed to avoid speculation in /r/AskHistorians, but unfortunately matters of Carthage leave little choice otherwise.

If you have further questions, I'd be happy to do my best to answer them.

Cheers.