Is it possible to artificially select for flight in pigs?
Intro course to evolutionary biology
I doubt you can get much from the below answer. At the end of the day, the only thing that would really allow you to increase your knowledge is probably an intro course to evolutionary biology such as Understanding Evolution by UC Berkeley for example.
Question

Is it possible to artificially select for flight in pigs?

If by 'artificially select' you refer to selection on available genetic variance, then No, it is not! You'll need plenty of new mutations and it would take a very long time.
Selection
You cannot select for something that does not exist. Selection requires pre-existing phenotypic and genetic variation for the trait of interest. No pigs are flying today, so you cannot increase the frequency of individuals flying by selection.
You will need to wait for mutations that confer such flying ability. Of course, there won't be a single mutation that turns a pig into a flying pig. Simply because flight is really not a simple adaptation for a pig! There are few species you could have chosen for which flight would be harder to think of! You are going to go on a long step-by-step procedure, fixing mutations one at a time by selecting every one of them and that will probably take hundreds of thousands of years or maybe millions of years.
Step-by-step procedure
I suspect you would consider using their front limb for flying. Here is a potential and extremely simplified step-by-step procedure. Of course, if you were thinking of pigs flying using their ears, the procedure wold be drastically different!
You should probably start by attempting to modify their limbs then. You can maybe try to start by selecting for individuals that are better able to manipulate objects with the front limb. Also start selecting for lighter bodies. Also, remove any selection for the ability of fast displacement or moving in the mud as that would select for their current front limbs. Start with some very very simplistic manipulation and increase up to eventually ending up with individuals that have pretty flexible front limb. Make sure to select for front limb that can move perpendicular to the body axis.
Then I don't know if you should aim to make wings out of skin or out of hair-feather like structure. If you're aiming with feather-like structure, you can try play it out with sexual selection just like it evolved in birds. Let's say you're choosing skin wings. Then, maybe selecting for those having broad and thing front limbs might be a good way to go. In the meantime, you've reached anything like that, you probably managed to reduce the body size of your pigs to the size of a mouse with a very elongated body.
Select for jumping abilities and then slowly for flying abilities. You've got flying organisms who's ancestors were pigs! Be aware nobody is going to fund such a useless and incredibly long experiment.