I don't use flikr or photobucket or any other photo sharing site so I might not be that helpful, but here goes,
I'm assuming you're on a PC - but you could make the graph or section of the spread sheet you want to share large on the screen, press the print screen button (typically above the Delete and Insert buttons). Then open up the Paint program in the Accessories folder under the start menu and paste (Ctrl+V). An image of you screen should be pasted into Paint from which you can crop and then save the file as a .jpg, .bmp or some other image format for uploading to a file sharing website.
Here's a wiki-how on doing the same thing in case any part of my explanation is confusing
http://www.wikihow.com/Take-a-Screenshot-in-Microsoft-Windows
Also I haven't used it much, but google has spreadsheets that can be shared. I have no idea how their graphing abilities go, if they're even available.
http://spreadsheets.about.com/od/tipsandfaqs/qt/share_google.htm
Good Luck!
EDIT - I just checked out Google Spreadsheets and it looks like there are several options for producing figures, with the ability to generate a URL that goes directly to the spreadsheet and graph, this might be your best bet.
EDIT for Jim Z - I think the problem you're talking about is in copying data from an online space delimited source into excel columns? Pasting the data in and then going "data" section of the ribbon in Excel, click "text to columns," click "delimited" and then the manner in which the data is delimited - be it space, comma, tab.