How will the censorship process be implemented in the application?

I think most videos will be monitored by moderators. Or the most popular video. Then it will be easy to find forbidden content.
We will likely establish several distributed and open access systems to aid with decision making rankings and user experience. The idea is that all the participants should have the best possible information at all times which includes, but is not limited to, results of PoA ( proof of availability ) challenges, video demand statistics, copyright and content id tags and basic telemetry.
If a material is found by the community copyrighted or not family friendly it will recieve a tag and the hosting node would not want to host copyrighted material, the uploader and the hosting node ( if he continues to host the content ) would recieve a flag.
There will be an order book held and a real time bidding between content creators and hosting providers. Each video will be stored on at least three distinct nodes to ensure the video is not lost. Each content creator will likely receive personalized offers from potential hosting providers, primarily influenced by popularity and risk profiles. To make this process easier, as well as to aid in matching the particular content creators with the optimal hosting providers, we should aggregate additional information based on usage of the Viewly app, such as viewership statistics (timing and frequency of views, average per-country aggregates) and the risk profiles (content id tags, copyright flags, and/or other disputes).
The price of storage will only be a small proportion of earnings for popular content providers, a small price to pay for storing videos with high intrinsic/emotional value and too expensive for low quality content and/or spam, ultimately eliminating the surplus of unpopular and/or spam videos.
The selected host will issue a bond (e.g. 20% of the annual hosting price) as a collateral for actually storing the file. If the hosting node fails a Proof of Storage (PoS) or Proof of Availability (PoA) challenges, they will lose the bond and and the offer to host this video will re-enter the marketplace.
In the event where content is purposefully discarded, both the bond and remaining funds in the contract are burned. The hosting provider forgoes the bond for the sake of aversion of potential legal liability, and the original uploader loses the remaining funds in the hosting contract. The hosting provider also suffers a small loss in their reputation score.
Of course nobody would stop you to spin up any kind of website based on the infrastructure and host your own materials but you would do so at your own risk.