I believe that Pakistan would have access to both the F-35 and FC-31. US State Dept. didn't bat an eye before approving F-16 sales to Pakistan, and it didn't really matter to the US that the Chinese were key allies with Pakistan and could have pressured the PAF to allow it to look at the F-16's "secrets". With Trump's recent Twitter backlash against Lockheed-Boeing (which apparently cost the companies more than $4B), the manufacturer may very well push for exports beyond the United States' usual clique of partners.
The advantages of purchasing the F-35 (vs the FC-31) would be that the PAF would have a ready-to-go fighter that is highly advanced and that Pakistan does not need to share a burden of the developmental costs (unlike first-tier partners like the UK).
The advantages of purchasing the FC-31 (vs the F-35) would be the platform's lower price (although not quite toe-to-toe with the F-35), modularity (the entire project can be customized for particular buyers), its ability to datalink with existing stocks of Chinese-produced weaponry & aircraft, and equal export rights for Pakistan (since Pakistan would have to pay a share of the developmental cost).
The biggest hurdle is not the US' willingness to sell but rather Pakistan's economic ability to buy.
