In Microsoft Teams, there is a general chat feature, but also there is a meeting chat feature particular to the meeting that you are attending.
In the general Teams chat, you can press Control + N to start a new message.
In the Teams meeting chat, you need to Tab to the meeting controls and then use the Left and Right Arrows to find the Chat button and press Enter.
Note: For screen reader users, Chat is announced as the Show Conversation button.
In both Chat features, you can type your message and press Enter to send.
At this point, you can Up Arrow to edit the last message you sent, press Enter to accept or Escape to discard the changes (Tab to Discard button and press Enter).
You can then use the Up and Down Arrows to read all the messages in the conversation during the meeting.
Press Tab to go to compose another message while in the Chat panel.
To close the Chat panel in the meeting, Tab to the meeting controls again and then use the Left and Right Arrows to find the Chat button (aka Hide Conversation) and press Enter.
Note: At the time of writing this shortcut, we found that JAWS was the only screen reader that works fully with the Chat feature in a Microsoft Teams Meeting.