There are two settings that affect JPEG file size, resolution and compression. Experiment with both these settings until you get a balance between the two that works for you. All other things being equal, I usually compress my images more rather than resizing them more, however Flickr has size limits that may affect your choice here. Always remember to keep an original uncompressed and unresized copy of your photo as well!
When you save an image as a JPEG, the quality of the image is degraded in order to make the file smaller. You can control the filesize versus quality tradeoff in photoshop when selecting
Save as... and choosing the JPEG format. You will be prompted for a compression setting. I never set this to more than 10 and neither should you, and settings down as low as 8 are generally satisfactory for me. When you set the JPEG quality, photoshop will estimate what the resulting filesize will be, enabling you to tailor this setting for the desired file size:
Resolution is the size of your image in pixels (or megapixels). My 550D saves images at 5184 x 3456 pixels, which is almost always way more than I need. For the purpose of posting to Flickr, unless you have a Pro account the practical maximum dimensions is 1024 pixels along the longest size, so there is little point in having a larger image than that. You can reduce filesize by resizing your image to a smaller size by going to the
Image menu and select