In the United States (and likely in other jurisdictions) the copyright holder has the exclusive right of "public performance" of the work, which includes exclusive control over broadcast and digital presentation of the work.
See Aereo for an example of a U.S. company that tried to challenge this exclusive right in a digital context and lost: Aereo captured over-the-air television broadcasts and presented them via an online service. The Supreme Court ruled that this violated the exclusive public performance rights of the copyright holders of the broadcasted works.
The work's availability as free of charge from the copyright holder is not relevant, as we can see in the above case. Aereo lost, and they were repurposing works physically broadcast for consumption by anyone who could pick up the broadcast signal.
By contrast, if you want to use a link to point people to the location of a video on the Internet that has been legally offered by the copyright holder, there is no law stopping you from doing so. Also, you might be able to serve a webpage that uses an iframe to frame the original source (though the case law in this area is somewhat conflicting), since your page that includes the HTML
<iframe src="..."> is in no way a derivative of the framed page. However, you could cause a trademark violation if you surround the framed page with your own branding and confuse the true origin of the video.
If the video you are linking to is an obvious case of infringement, posted without permission of the copyright holder (e.g. the latest Game of Thrones episode hosted on
pirateallthemovies.foo), then systematically helping people find these sorts of illegally-posted resources can make your liable for contributory infringement.
Whether or not merely distributing such an app (versus using such an app) is illegal depends largely on whether the app automatically performs copyright infringement for its users and whether the app has substantial non-infringing uses.
- If the app's author makes the app intentionally direct users to infringing resources, then the author is liable for contributory infringement.
- If the app circumvents DRM that controls access or copying, that is likely a DMCA violation in the U.S.
- If the app merely plays videos from an arbitrary user-defined server, then it may have substantial non-infringing uses: it's just a video player app that plays videos that servers offer on the Web.
- By contrast, if such an app hard-coded by the author to use a particular server that consists substantially of infringing material, that's the contributory infringement case.