As I've written, I don't think inequality in and of itself is ever unjust. The bare fact that A has 5 billion dollars and B has 40 thousand dollars and C has 5 dollars is not unjust - though I recognize saying as much involves some ash on the tongue for a lot of people.
That doesn't mean I think people - particularly wealthy people - have no Christian duty to each other. I believe they do, and that this duty involves (among other things) giving up wealth to help those who need it. But here, simply having wealth at one's disposal - not inequality, but the command of wealth - is going to be one of a number of factors in play in determining who has what duty.
More importantly, I think it's a mistake to play the game of thinking in the broadest possible categories, where 'the top 1% has a duty to the 99%'. It's a little like saying that 'men have a duty to children', as if all men have a duty to all children - even if you argue that all children ultimately had a father, it's still an insane way to draw those lines. Now, saying fathers have a duty to their offspring? That's better - more on target. Now we're not describing the relationship of one broad class to another, but individuals to individuals. It's more tractable, and in that case, more natural.