I'm planning to buy a Canon PowerShot SX280 HS with an SDHC memory card. If I connect a 30-pin card reader to my iPhone 4, would I be able to upload the photos from the card onto the phone and then upload to an image host such as Flickr (presumably one that has an app with an upload function)?
You could try something like an Eye-Fi SD card - http/www.eye.fi/
You would need to install the Eye-Fi app on your iPhone if you choose to use and Eye-Fi memory card.
The card appears to be compatible with the Canon PowerShot SX280 HS - http/support.eye.fi/cameras/canon/powershot_sx280_hs