Looks like Speed Dial for firefox and Speed Dial for chrome are made by two different developers. The Firefox version allows you to import\export data but the Chrome version has no such options.
In Firefox Tools >> Add-ons >> Speed Dial Options >> Actions there are options to import, export, restore from backup, etc.
In Chrome going to Extension >> Speed Dial Options it only allows you to make cosmetic changes to the start page (spacing, theme, etc).
So currently it doesn't look possible.