I was an ECE in 2020 in NS. Due to COVID-19 shutting down child care centers from March - June and continuing to be paid, can I claim work from home expenses?

Yes, if you were required to work from home, you can claim the flat rate if you don't have a t2200s or t2200 from your employer. 

If you were on paid leave - being paid but not required to work, then you can't claim employment expenses.