As far as I have been able to find, no myth specifies anything tantamount to these siblings being sextuplets. There is, however, one ancient story which claims that four of them were twins, that is to say that there were two separate sets of twins, and that Zeus was one of the older set thereof.
A Different Sort of Multiple Birth
The 4th-century-BC mythographer Euhemerus wrote extensively under the notion that the gods, originally, were merely human rulers, conquerors and heroes whose great deeds in life caused them to be revered to such a degree that, after their deaths, they were venerated as immortal beings. This technique of rationalising the myths has, from him, come to be known as euhemerism.
Euhemerus wrote a theogony which does not survive but, as summarised by Wikipedia, "Ennius translated Euhemerus into Latin about a hundred years later, and a passage from his version was in turn preserved by the early Christian writer Lactantius."
According to this rendition, which Lactantius narrates in his Divine Institutes 1.14, Hestia had two sons: Kronos [Cronus] and Titan; and two daughters: Demeter and Rhea. Titan, who was older than Kronos, should have become king, but then, because Kronos was more handsome, all the three women in the family supported his bid to the throne.
The two brothers came to a compromise. Kronos would become king after all but any male child that he had would be done away with so that eventually the children of Titan would inherit the throne after their uncle. Kronos was married to Rhea, and their firstborn son was killed, presumably as soon as he was born. He remains unnamed, but after that Rhea gave birth to twins: Zeus and Hera.
Next up, Poseidon was born alone, followed by more twins, called Hades and Glauke (or, per the Roman names they are supplied with by Lactantius, Pluto and Glauca). All the boys were hidden from Kronos, while Glauke, who seems to be otherwise unknown, "then died young."
The More Common Tradition
In the more mainstream version of the mythology, however, it appears to be almost certain that Zeus, at the very least, was not the product of a multiple birth. The accounts given by certain different writers regarding this can be read as being ambiguous enough to imply that Zeus, the youngest of Rhea's offspring, was born separately from his five older siblings, and that these other five were quintuplets. There is, however, no narration that makes any such explicit claim about a multiple birth prior to Zeus.
The most clear-cut statement on the Question would be from the Roman poet Ovid's Fasti 4.199-203, which says that Kronos, out of fear regarding the prophecy about his own kids overthrowing him, "devours his offspring as each was born, and entombs them in his bowels."
Resulting from this, it came to be that
saepe ["often/ frequently"] Rhea complained of totiens fecunda ["much pregnancy" or "frequent fruitfulness"] but no motherhood, and
she was aggrieved by her own fertility.
The very next words go on to say that then “Jove [i.e. Zeus] was born”, whereupon Kronos was tricked into swallowing the stone decoy.
A Greek author, Diodorus Siculus, records in his Library of History 5.70.2 that
Kronos pleonákis ["time and again" or "repeatedly"] did away with
the children whom he begot...
Going by those two accounts, particularly in the former, it would mean that Rhea conceived and gave birth on at least three different occasions, with Zeus in particular having his own birth-date exclusively apart from any of the rest of his siblings.
According to Strabo's Geography 10.3.11, Kronos was eithismenon, "accustomed," to swallowing his children, and that Rhea, apparently in consequence of this, contrived to hide Zeus's birth (and perhaps the whole pregnancy itself, "her travail") from the child's father.
Apollodorus' Library 1.1.6 narrates the incident using similar terms to those of Strabo in that Rhea seems to only become “big” or “heavy” (i.e. pregnant) with Zeus after the first five children (all listed by name in the previous line) have been swallowed by Kronos.
Going all the way back to Hesiod's Theogony (Lines 464-492 thereof), a good amount of time appears to have passed between Kronos swallowing his children and Rhea being ready to give birth to her lastborn child Zeus. In between the descriptions of the first children being devoured and Rhea's preparations for Zeus, the Titaness grieves, then plots with her parents about how to rescue her last child, and is sent by them to Crete, where she delivers Zeus.
Finally, there is an Arkadian [Arcadian] version of the myth reported to us by Pausanias in his Description of Greece 8.36.2, which claims that Zeus was born on Mt Lykaios [Lycaeus] in Arkadia [Arcadia]. Before this, however, Rhea, when she "was pregnant with Zeus," had fled to another Arkadian mountain, named Thaumasios (the "Mountain of Wonders"), where she enlisted a squad of Gigantes (Giants) to be her bodyguard "in case Kronos should attack her," and these were led by a certain Hoplodamos (the "Armed Man"). It was therefore also on Mt Lykaios that Kronos was deceived and swallowed the stone substitute for the baby.
The amount of activity, scheming and travelling in which Rhea engages in the Theogony and in this passage of Pausanias, in between the births of her first five children and that of Zeus, strongly suggest that this was not envisioned as taking place all on the same day.
Somewhat closer to Euhemerus' version, the Roman writer Hyginus (in 139 of his Fabulae), makes mention of an unusual account in which Hera is apparently all grown up by the time Zeus is born and it is she who rescues Zeus by taking him to Crete Island to be there hidden away from Kronos. Meanwhile Hades and Poseidon have also already been born, and their father has cast them, respectively, into the Underworld and into the depths of the sea.
If, from this, one were to infer that Hera, Hades and Poseidon, at least, were fully grown before Zeus was born, this might settle the issue in favour of the conclusion that they could therefore not have been sextuplets (or even quadruplets if we counted these three together with Zeus).
There is, however, the fact that the childhoods of the gods can be unusually brief, or that they are capable of incredible feats within mere hours their birth, as attested particularly in the tale told of how Artemis was born and very shortly thereafter became one of the midwives aiding in the delivery of her own twin brother Apollo.
So, with the exception of Euhemerus (via Ennius and Lactantius, as above), there is no ancient source which explicitly denies that Zeus and his older siblings were sextuplets, but the most detailed narrations of their story appear to me to be intending several separate births.