I use skype for business at work.
I am not a big fan of chat in general so I used the settings to have
unread chats show up in my exchange mail account.

I can use chat with NVDA, it requires some object navigation in the
chat pane instead of just arrow/tab navigation. Once in the chat pane
use the object nav read by line and line navigation (num pad in
desktop layout).

FWIW my employer uses office 365 so our install is newer than 2015.
Skype® for Business for Office 365 MSO (16.0.11328.20144) 32-bit

Mike