DSLR or Mirrorless for video?

I was looking at picking up a new camera for shooting movies and what I want to know is: the 1080p on the Nikon D5300 worth the extra cash over the 1080i on the D5200?
Also I was looking at the Sony Alpha a6000 and really like the specs, but the semi articulating screen is a real put of for me. Is there a way around this via a smartphone app or something.
Maybe next gen I'll go mirrorless. What do you think?

Neither of those.

If you want to shoot video, get a dedicated video camera. The fact that most stills cameras can now shoot video doesn't make them a good choice for the task. A proper HD video camera will make it far easier to shoot movies and will reduce your workload in doing so. Many video cameras can also shoot still images, but in the same way are far less suited to the task than a dedicated stills camera.

Going back to your question, progressive scan gives a better output quality than interlaced, so 1080p is a better choice than 1080i.

Mirrorless cameras can be fine, they're lighter and more compact than SLR models and as the lenses can be mounted closer to the image sensor they can also be smaller and lighter. But they are a lot more battery hungry and few EVFs compare well at this time to the direct optical viewfinders of SLR models.

I don't fully understand your comment about the semi-articulating LCD screen of the a6000. It's a hardware feature which you can use or not at your choice. No app can turn it into a more reliable non-articulated screen or into a far more fault-prone fully articulated screen. I understand the benefits of articulated screens but it's a feature I've rarely used and I have a drawer full of cameras I no longer use because the flexible printed circuit boards which feed them have cracked after just a couple of years or so and very little use of the the articulated joints. If you want maximum reliability then go for a fixed screen, but if it's a risk you're happy with or if you plan to shoot video regularly with a camera you've chosen primarily for shooting still images then it might be a sensible choice. A dedicated prosumer video camera will always have an articulated screen and EVF but the internal engineering will normally be designed far more robustly than on a stills camera as it's a feature which will be in constant use.

Normally I'd look at a Sony SLT, like the A-58, but if video's all you want, look at camcorders.

If you want a DSLR with video as a high priority, and you don't like the Sony SLT cameras, you should consider the newer Canons--the T5i or 70D.

Lots of talk about various brands most are about personal preference. For me it's the Canon t3i. I get excellent results with mine but there are accessories that you should buy to improve your results, regardless of the camera you choose so know that in advance.

Buy a camcorder!

The right tool for video is a digital camcorder. If you're one of those persons who believe otherwise, the next best thing is an SLT.