If you don't want to install FNAF Ultimate Custom Night game online, you're out of luck.
The game must be downloaded and installed on your PC, as Scott Cawthon (developer) does not develop flash games and there is no official confirmation of this rumor.  All other resources that offer to play UCN game online are engaged in a deception of consumers. You can get this game from official sources, links to which you will find on the download page.