I sometimes have to use the Skype for business app and I find that if I click on the link in an email or on my calendar it usually fails to open correctly. I then end up trying to use the web app which rarely works.
By accident I've found a way to get the Skype for business app to work regularly.
Firstly don't click on a link in a an email of calendar, instead copy the meeting URL.
Then open the Skype for business app, you should see the window below. Don't add your email instead click the "Join Meeting as Guest link highlighted in red below.
This should take you to the following window, don't try to sign in using the Office 365 account. Paste the meeting URL into the box, then enter your name and then click Join as Guest. This has worked every time for me.