Compression shouldn't affect sharpness very much.
What really matters is the actual size in pixels at which you want to display in flickr. You can then resize the original to suit. The 'native dpi' setting is not strictly relevant, but most monitors display at about 72dpi and it is normal to use this by default for web images. Also make sure that you convert to sRGB colourspace for the web (and any other applications that are not colourspace aware.)
I've not used DPP for ages and certainly not to resize for the web, but can I make a suggestion? If you convert to full-size TIFF or JPEG as you would normally, and then resize using the Faststone Image Viewer which is free and seems to do a pretty good job of resizing, as well as being a good browser and slideshow utility.
FastStone Image Viewer, Screen Capture, Photo Resizer ...
You can also use Photoshop, Paint Shop Pro or any decent image editor for resizing. I believe that Photoshop has a 'Save for Web' function but this seems to strip out the EXIF data which you may want to keep.