How can I protect my phone against Krack Attacks if no updates are forthcoming?
If your phone manufacturer or service provider will not push updates there are a few things you can do (some already mentioned in comments.) From easiest to hardest, these would be:


turn off wifi and only use mobile data (easy but possibly expensive, depending on your plan)
update your own wifi router, and only use wifi on your network and others that are confirmed patched
buy a new phone (They will have updates - could this be an excuse to get a new one?)
use a different kernel. LineageOS is generally leading edge, as Једноруки mentioned, so it will have an update very soon
write your own kernel. Tools exist to help you work on Android kernels, and the update required is publicly documented.


The thing to remember is that currently it is unlikely to happen. Yes, once the exploit is out there and spreading, you'll want to be on a patched phone, but don't panic about it today. And the attack is mitigated by VPN's, https etc.

For technical analysis and up to date security commentary on this, look at the Krack tag on Security Stack Exchange.