People kill me with these threads. We get into swirling of yeast, holding your mouth a certain way, sacrificing chickens to voodoo spirits... if it's been two weeks and the beer is flat, I'm not in the least surprised. Carbonation is not a linear process (i.e. X carb at day 5, Y carb at day 10, Z carb at day 21).
Every yeast strain/recipe combination can be different. If your yeast are tired due to high gravity or less than optimal fermentation conditions (underpitched, temperatures not the best), they could take longer.
Some people have carbed beer at two weeks. Yay for them! But here is the truism you see repeated dozens of times every day on BHT: three weeks @ 70 degrees F is the baseline for typical beers. Higher gravity or lower temps can make this take longer. Some beers will take longer, anyway.
If you added priming sugar and mixed it well, the beer WILL CARB UP 100% OF THE TIME. A bottle opened at two weeks is a crapshoot; even if it's carbed, it's probably still green. If it's flat at three weeks, wait another week or two. If it's flat then, wait another week or two. You can swirl till the cows come home, but the effect will be minimal - the yeast wil be done when they are done. There is way more than enough yeast in suspension to carb your beer.
Go brew another batch and quite worrying over this one. It'll be done when it's done.