The Veil of Ignorance is similar to John Locke's "Veil of Perception", suggesting that human understanding is like 'a closet wholly shut from light, with only some little openings left, to let in external visible resemblances, or ideas of things without'. Going on about how the way we see things is limited, which is what the Veil of Ignorance is saying just in a different sense. Its not describing how we see the world, but how we see people. More so, people's inability to see how it is to live as another person.
I don't know enough about Kant, apologies.