If I use Blue's Tactics and then later KO an opponent's Pokemon, do I take prize cards and then draw until I have 8 or can I choose the order this happens in?
You take your Prize cards first, and then at the end of your turn you draw for Blue's Tactics.
Source: TPCi Rules Team (2019-08-01)

Relevant cards

Note: All applicable cards may not be listed below.
SM11_188
SM11_188
SM11_231
SM11_231