There are ways to use a countries colours that are more creative then others.
Two examples I see of patriotic logos are the Columbus Blue Jackets (NHL) and Winnipeg Jets(NHL). I am assuming that a"Blue Jacket" is some sort of military uniform. Similar to the New England Patriots (NFL) logo. They've both worked some flag elements in with the military theme. I think that works, since the concepts are linked in my mind (no military with out a country to represent).
For the Jets' new logo, they've got the a gray jet superimposed on a red maple leaf. I see less integration between the jet element and the red flag unlike the Patriots and Blue Jackets. Still willing to give it a pass since there is the link between Avro Arrow and made in Canada.
The Houston Texan's logo takes it up a step further, with no flag whirling around, its part of the coloring of the buffalo with a star replacing one of its eyes. An example of an logo that integrates red, white and blue poorly is the Washington Wizards logo. They need to go back to the drawing board on that, it's a fragmented mess.
The problem that both the Vancouver Grizzlies and Toronto Raptors ran into was too many colors going on at once. The 2008 update of the Red Dinosaur logo, replaced the purple elements with black, and thus reduced the total number of colours used in the logo by one. The Raptor Claw took it much further but cutting things down to two. The Memphis Grizzlies logo uses three shades of blue, and I thought that was a creative touch. The recent trend in the NBA has gone towards team logos that are created using two colors if possible.
(Description of how the above graphic was created, and the significance of the circles can be found at the above link. There is one for the NFL, and MLB as well. Please click on the image for a full size version that's easier on the eyes)
A good example of two colour use is the Golden State Warriors logo. Able to work the bridge in there, plus the ring around it, while sticking with blue and yellow. An example of too many colours is the Minnesota Timberwolves and Dallas Mavericks logos. Why can't we just take the fact that the timberwolves live among trees on faith, do we really need the row of pine trees there? Less is more.
What sorts of logos in professional sports are you a fan of and what about them makes them stand out to you?