Why does my dslr's flash work in landscape orientation.but not in portrait?

Built-in flash on my Nikon d3100 works great when oriented horizontally, but meters the far left side of the frame when I shoot vertically (portrait) orientation.

I'm a bit confused about your "meters the far left side". Metering is through the lens, so it doesn't favor left or right. It may favor portions of the scene if you're using Matrix Metering. Try spot or center-weighted metering.

One thing, if you're talking about the left side being brighter, and you have your lens hood on, the lens hood can cast a shadow, which might make your subject darker.