First discuss it (in private) with the Chair.
It should be part of their role to ensure that 'airtime' in the meetings isn't dominated by one person.
If there's a discriminatory aspect to this - if person X is dominating the meeting because they perceive themselves to be superior to the other participants or more entitled to speak because of their gender, race, etc versus that of the other participants - then this applies even more.
On the other hand, it is possible for people to do this - dominate the 'airtime' of a meeting - without really intending to, particularly if they're very enthusiastic about their contribution. They might (perhaps) not realise that they're denying other people the opportunity to speak - so a good first option might be for the Chair to have a quiet word with them in private (outside of the meetings).
please include a description of how I would respond when I am one of the two speakers
OK, so if I understand correctly, when you're speaking, you're railroaded into silence by another person, and they do this constantly to you and to other board members (have I got that right?).
So what you need to do is find an assertive way to respond which allows you to make your point.
Address the person interrupting you directly, using their name:
"John, could you let me finish please?"
"Jane, I'd really like to finish what I was saying".
"John, please could you allow me to finish speaking?"
If that still doesn't work then address the Chair, using their name:
"Dawn, I'm not being allowed to speak here. Could you please ask Jane to wait until I've finished, and make her contribution then?"
At that point, if the Chair and the rest of the meeting don't do anything then you really have a dysfunctional board... in normal circumstances the steps above would work quite reliably, here in the UK (other cultures of course may differ).
how I may assist other board members when they experience this behavior.
Interrupt the interruption with:
"I'd really like to hear what Joe was saying".
Interrupt the interruption again with:
"John, I really do want to hear what Jane was saying. Could you wait until they've finished?"
Appeal to the Chair on behalf of the person who's not being allowed to speak:
"Dawn, I think it's only fair that John be allowed to finish. Could you call the meeting to order please?"
Things that can help:
Talk to the Chair before the meeting.
Talk to the other participants before the meeting, see if they think it's a problem too, agree that you will support each other in making sure that everyone gets a chance to make their contribution.
Sit next to the Chair so that you can make yourself heard to them without needing to raise your voice.