No, pigs will not be kosher food, not even when pigs learn to fly -- well, at least not until the Messiah comes or science finds a way to change the pig from a pig into something else a bit different.
The Torah prohibits animals that can be eaten based on physical characteristics. Leviticus 11:1-32. A kosher animal among mammals must have a cloven hoof and chew its cud. Lev. 11:3. The Torah goes on to give us examples: a camel, a badger, and a hare are forbidden because they chew their cuds, but do not have a cloven hooves. Lev. 11:4-6. The swine is given as the opposite case because it has a parted hoof but does not chew its cud. Lev. 11:7. The Torah gives us no other reason, certainly no health reasons. And I am unaware of any health reasons that make it unsafe to eat camels, badgers or hares.
Moreover, it is not within our authority to change the Law if we wanted to. Deut. 4:2 states that we can neither add nor subtract to the Torah.
The story could change when the Messiah comes and as for that there is some dispute. The midrash on Lev. 11:says that the reason that the pig is called “chazir” is because in the future Hashem will return (lehachzir) the pig to Bnei Yisrael and permit it to be eaten. According to many Achronim the midrash is to be taken literally; pig will be kosher in the future. The Rama Mipano (Asarah Mamaros Chikor Hadin 4:13) explains that Hashem will make the pig chew its cud, thereby making it kosher. Critics of this point, however, argue that there is a rigid guideline that prevents this, citing the Gemara at Bechoros 5b, “hayotzei min hatamei, tamei – anything that comes from a non-kosher animal is not kosher.” Therefore if a non-kosher animal gives birth to a kosher animal (which has the kosher signs), it is forbidden to be eaten.
According to Rabbi Raphael Fuchs, Rambam (Maimonedes) would say that a genetically-engineered pig that chews its cud would also be prohibited because it is not one of the ten explicitly-permitted animals mentioned in the Torah. Hilchos Machalos Asuros 2:3. Any other animal (even if it has the kosher signs) is prohibited to be eaten because it is a lav haba michlal assei (when the Torah says you should do this it is inferred that it is prohibited to do otherwise – and the Torah says to eat these animals). It is for this reason that humans are prohibited to be eaten, since they are not one of the animals explicitly mentioned in the pasuk. However, if you hold that way it would seem to me that you also can't eat turkey because it is not mentioned in the Torah.
So, how do we explain the midrash? The Radvaz (Teshuvos 2:828) explains that the midrash is not to be taken literally; rather it should be understood that in the future Bnei Yisrael will eat mashmanim, as if eating pig was permissible. Rabbeinu Bichaiya also explains that the intention of the midrash was not to say that pig will become permitted for consumption in the future, but rather that the midrash is referring to the kingdom of Edom (which is referred to as the chazir) – that Hashem will eventually return (lehachzir) on them midas hadin (judgment). The Ritva (Kiddushin 49b) explains that the midrash is referring to Amalek.
There are opinions that suggest that a genetically-engineered pig (made with kosher signs) could be kosher if it was born of another genetically-engineered pig. This assumes the rabbinic principal that something born of a forbidden item cannot become permitted. Menachos 21a (example, boiled animal blood would technically be kosher according to the Torah, but since blood in its natural state is forbidden, rabbinically, we can not eat boiled blood, either). But once genetically-engineered pigs are born, they would become permitted to be parents of kosher little pigs. See this article from the Jewish Press.