It would also get its own unique IP, this jail.
Then I fire up firefox inside that chroot jail and use it to visit some websites ... and then I can wipe the whole thing out and redeploy again later, starting from scratch.
I don't need to trust incognito mode, I don't need to trust wiping cache or tabs talking to each other (or not) and I can worry a lot less about browser level exploits.
I can even put in firewall rules so that my "banking" instance can only talk to boa.com and scotttrade.com (or whatever).
It's totally workable (and I have done it) with vmware. Make a "bank browsing" VM and revert to pristine snapshot every day. The problem is that this is terribly heavyweight and overkill when I don't need a full blown VM.
It's not even really a browser issue - the real issue is, how do you jail a GUI application in X such that that window is in a chroot jail, distinct from the rest of your desktop?
The entire concept you're aiming to set up is terribly heavyweight and overkill. If you're knowledgeable enough to be discussing VMs and chroots, you must realize that what you are proposing is being careful to the point of paranoia à la tinfoil hat. Those of us who know how to stay as safe as possible via "basic" methods of security should be sleeping soundly knowing we're already in the top 5-10% of consumers. Install OS security updates, use a virus scanner and firewall, don't install pirated software (more likely to contain malware), and you're better off than most people by a significant margin.
You're talking about barely making a dent in the chances of your credentials or sessions being compromised. Private browsing, a separate browser instance, a VM, or chroot makes no difference if you have malware with a keylogger on the host system. Give yourself a break, realize that there is no such thing as "perfect security", and stop worrying so much. The amount of energy you're pouring into "banking safely" is not a sane endeavor. It serves no useful purpose. You could be investing this time and energy into something far more likely to improve your quality of life (eg: family, friends, health, etc.).
1 - Create a container (Docker, Jails, maybe even chroot)
2 - Assign an ip to the container, NAT to it
3 - Install firefox on that container
4 - Run a SSHD server, enable X11 forwarding
5 - Mount the relevant container's folders to your root fs (eg: map $CONTAINER/.mozzila and $CONTAINER/Downloads to $HOME/jailed-browser/)
6 - Add an ssh config for quick alias
7 - Run `ssh container firefox` and profit
Here's a nice example using FreeBSD jails (I remember following this tutorial, everything worked out fine):
My experience with it, though, wasn't great. X11 forwarding through SSH was quite laggy (even after performing some optimizations on the connection). Good luck if you want to set-up audio/mic support. It's a nice solution for a one-time banking login, not for day-to-day use.
Thank you very much! I will give this a try immediately.