Looking into it a bit... it seems Netflix used to have an API but they've deprecated it and closed it down at this point which is disappointing.
However - there are unofficial alternatives apparently but not sure how they work if there's no actual Netflix API for them to use! Maybe they're web crawling to build their own database.
uNoGS API "Unofficial Netflix Online Global Search API" seems to be one.
There's Streamzui which is for Amazon Prime Video
UTelly API covers tons - Neflix, Amazon Prime Video, Amazon Instant Video, iTunes, Now TV, TalkTalk TV Store, Google Play, BBC Iplayer, All4, My5, Rakuten TV and ITV Hub.
Seems like UTelly would be awesome to play with and I wonder if "Rakuten TV" would incorporate Viki.
For Viki directly they have an API currently on v4 which you can google (it won't let me link).
Are there any other good recommended sites that people stream from? It may be that with enough momentum particularly via the major streaming sites noted above, getting other sites to add an API may be a possibility (it's not a hard request to fulfill on their side really).
Anyway hope this helps. I might download that UTelly one and have a play, that looks intriguing!
Matt.