No, it is not illegal. However, it is almost certainly a violation of your school or workplace’s computer use policy.
There is no single "magic link" that works forever. When a game goes viral, firewalls update to block specific URLs. However, here are the three best methods to bypass restrictions and find a working link: blacket unblocked link
Blacket is an open-source clone/private server of Blooket. Because it is hosted on different domains than the official blooket.com, network filters often fail to block it. It also frequently gives users "moderator" powers or infinite currency in its test environments. No, it is not illegal