If Cinccino with the "Smooth Coat" ability also has "Rocky Helmet" attached to it, can I choose to activate Rocky Helmet first, and then flip for Smooth Coat?
You would need to know whether Cinccino takes damage or not in order for Rocky Helmet to work, so in this scenario you would have to flip for Smooth Coat first.
Source: TPCi Rules Team (2012-03-15)

Relevant cards

Note: All applicable cards may not be listed below.
BW11_105
BW11_RC19
BW3_94
BW4_85
BW7_133
BW7_153