I still fail to completely see how saying a flat tax plan is inherently un-Christian. Yes, there exists massive potential for it to negatively effect the poor. It's part of why I'm personally against it as well.
However, a thing I noticed while looking at financial records for the church I used to go to (used to because I had to go to college) was that during and following the 2007 economic crisis there was a massive downgrade in giving, which led to a massive downgrade in the amount of outreach and volunteer work the church was able to do. With the general increase in taxes due to the Obama administration, the church was continuously hindered in its efforts to return to what it used to do volunteer-wise, even as the economy has recovered.
Now, I think that regardless of who is president and what our taxes are, the church has a responsibility to help the downtrodden. But if a much more right-wing tax plan were in effect, it would really light a fire under the butts of many Christians (particularly evangelicals), as money coming in wouldn't be quite as big a problem any more, as well as the additional weight of knowing that they, as members of the community, need to play a role in helping the poor, as the government isn't going to do that job. Considering that Trump was (is?) leading among evangelicals, they could definitely use the wake-up call.
Now of course, all of this is hypotheticals, and I don't think it's quite the best way to go about things. But it is the main reason why I typically vote Republican. And it's also why I'm a big fan of Kasich, as he's one of the more "normal" Republicans that's a sort of descendent from the 80's rather than the crazies that currently run the show now. Unfortunately, he won't win it, and the days pass where it looks more and more likely that the nomination will go to Trump or Carson despite terrible performances in debates (including this one), which means I just won't vote and just move on with my life.
Thanks for bringing up points. It's been helpful for me personally, if only to hash stuff out in my head.