I decied to encode the entire application state as a Base64 encoded string in the hashmark of the url. For example, a url would look like (note its truncated since they are very long):
knotend.com/g/a#N4IgzgpgTglghgGxgLwnARgiAxA9lAWxAC5QA7X...
Everything after the /g/a# is a stringified version of a json object that contains all the information about the flowchart. It gets stringified, then compressed, then Base64 encoded. I update the url on every graph edit, so copying the graph state is as simple as copying the url in your browser bar.
Here's the pseudo code for creating the url, and then later reading it:
const stateString = JSON.stringify(appState); // appState is a json object
const compressed = compress(stateString);
const encoded = Base64.encode(compressed);
// Push that `encoded` string to the url
// ... Later, on page load or on undo/redo we read the url and
// do the following
const decoded = Base64.decode(encoded); // same encoded as above, but read from url
const uncompressed = uncompress(decoded);
const newState = JSON.parse(uncompressed);
// Now load your application with the newState