The field and obstacles may change whenever you play Pennant Capture, so
it's not always the same, but once you get the hang of it, you'll recognize
the field right away.
Try to collect flags clockwise or counterclockwise. Once you make a round,
go back to the starting point. Going back to the areas where you missed
collecting the flags will waste time, and the opponent will likely get it
once you go back.
High speed and skill.
Yeah Gamefaqs has some pretty good tips on it.
Really it takes a bit of practise to get the hang of it. It took me forever to get past 30 in that game. Try avoiding the other Pokemon, especially if you have alot of flags. Personally, I only go back once I have at least 5-6 flags, instead of just 2 or 3. Do remember that if you're able to, you can hit the opponent to get 2 flags from them (or 1 if they only have 1), which really helps in getting to 31.
Using Pokemon with higher skill makes it easier to gather flag, but a bit slower to gather each one. Speed would make it less accurate, but faster in finishing a flag gathering 'round' (See the GameFAQs bit for round).