The short answer to this question is no. In fact, not only is it not possible to video chat with 3 separate devices at the same time, but it is not possible with 2 devices! You can login to multiple devices (for example, an Android phone and a computer) with a Facebook account. But when it comes to video calling, you can only call one of them.
Suppose you see all the messages that come to you instantly on your computer. Now when you try to make a video call with your mobile, you will not see anything in the PC version of Messenger. This means that it is not possible to watch this video chat via computer. But if someone calls you and you do not answer for any reason, after the phone rings, you will see Miss Call message on your chat page with him/her, on the computer. The same is true for three separate devices with one Facebook account.
But if you mean the question of how multiple people can connect with multiple devices via Facebook Manager video calling, the answer is different. You can make group video calls using the group creation feature in Messenger. Or when talking to one person, add other people to your call using the + button on the video chat page.
This application has a limit on the number of people who can be present in a video chat. But that number is so high that you can use Facebook Messenger as a good platform for video conferencing! You can add up to 50 people per video call. It does not matter how long you want to be video calling; you do not even need to have a Facebook account to be able to video chat! Easier than this?