Here is my flow for testing Cheogram WWW with orca in order to use most functions of the app. Please let me know if this doesn't work for you or you'd expect things to work differently.

There are five landmarks on the page: account navigation, search box, chat list, main content area, and message compose box.

You can press M and Shift+M to move between these, but note that the search box is a focus trap, so to move past it you need to do INS+A (go to browse mode) then quickly M or Shift+M. Or you can Alt+Shift+M to get the list of landmarks, arrow keys to pick the one you want, and jump right there.

To get to a chat, move to the Chat List landmark and then press tab to move through all the chats in the list. You can use the "Find or start a chat" search landmark (also accessible as accesskey + / which for me is alt+shift+/) to type a search first, then tab twice to get to the list, and then push tab once for each search result. Press enter to select a chat. Focus will move to the input box for composing a new message to send. Orca will announce the name of the chat and then the most recent message in the chat. If you want to send a message at this point you can just type and hit enter.

While you have a chat selected any new messages will be announced as they come in.

To read messages there are probably a lot of things you can do, here is what I do: use landmark navigation to select the main content area, this will take you to the top of the current scroll area. Then press P once to get to the message at the top of the page, the body (or first paragraph of the body if it is long) will be announced. From there you can use P and Shift+P to go up or down the messages/paragraphs. This may be sufficient for many purposes.

To hear the name of the sender and the time the message was sent, press down arrow from the last paragraph of the message.

If you are on a message then Shift+tab will take you to the menu for the message (to reply, react, etc) and shift+Tab again will take you to a button to open the sender's profile.