I don't know how to flip an image in gimp, but I do have other suggestions that could help. I'm a graphic design student, so I know some things about logo design.
If you're doing logo design, I would recommend using a vector imaging software. Vector images can be resized and enlarged without losing image quality. Adobe Illustrator is the software most commonly used by graphic designers to design vector images, however it is very expensive. A cheaper alternative is inkscape. It's freeware that can be used for vector image design. It's a little more limited than Illustrator, but an improvement over a bitmap image when designing a logo. I've tried it once before and it takes a little getting used to, but its fairly good for free software. If your logo is not too complicated, I'd recommend tracing over it in Inkscape or another vector imaging software. This will allow more versatility with image size and resolution.
If you designed your logo yourself, I'd recommend making sure it's not too full of tiny details because it can be difficult to make out small details on a logo when it's shrunk to a small size like it would be on a business card.