It looks like the sides are done first and then the top, but the top could also be fondant which would be easier so the 2 different colors of frosting won't blend.
It looks like the white part is fondant. Put the teal buttercream first and lay the white fondant.
My take...ice the bottom in BC...lay on the fondant...fondant or gumpaste pearls...RI dots and BC piping. I would use silk flowers as most every carnation you buy has pesticide residue.