Greece First:
Following by the countries in alphabetical order of the host country (Brazilian Portuguese)
Refugee Olympic Athletes (New this year)
Brazil
https://en.wikipedia.org/wiki/2016_Summer_Olympics_Parade_of_Nations
1 Greece (GRE)
2 Afghanistan (AFG)
3 South Africa (RSA)
4 Albania (ALB)
5 Germany (GER)
6 Andorra (AND)
7 Angola (ANG)
8 Former Yugoslav Republic of Macedonia (MKD)
9 Antigua and Barbuda (ANT)
10 Saudi Arabia (KSA)
In a completely different thread [his Member Blog] CAF asked a question about the Burundi team's entrance in the Parade:
I don't know the answer for sure, but I think I can make an educated guess.
Rio's Parade of Nations used literally every known trick from earlier opening ceremony parades, to make the process smooth and enjoyable for all:
A development of Sochi's technique of having teams do half-laps rather than full laps: parading up the centre of the arena, then back