If you are putting private keys in the browser (front-end) without making the entire app a "browser extension" encrypted or not, then you're potentially going to send that key back and forth over the wire or not?
From a security perspective I would keep these kind of keys on one side only, make sure it's either never transferred over any network or as least as possible (even with HTTPS encryption it's actually butt-easy to spoof a fake certificate and ssl authority-server when you control public hotspots and decrypt someones traffic, then there's XSS injection too). Storing private keys in the browser also makes you prone to accidental loss. LocalStorage, cookies and caches are wiped when you remove your internet history.
You might wanna check in with https://github.com/sammacbeth/dat-fox/blob/master/README.md.
What they did was to create a small helper app that one can install on their machine (in this case, it caches & proxies traffic through the dat network) and a firefox/chrome/etc plugin/site for the front. The plus of this would be that even if you remove internet history, whatever is stored is still there.