Hello,
Thank you for posting in the HP Support forum.
I don't think this is possible. Many years ago flash drivers were sold with drivers for old Windows, but not anymore. Nowadays flash drivers are automatically recognized on the new OS (NT based) such as XP/Vista/7/8, etc.
You can read the user guide of your flash drive -> http://h10032.www1.hp.com/ctg/Manual/c01726916.pdf and email the support (email inside) and see if they can provide you with drivers for Windows 98.
As an alternative, you can slave the HDD of this Win 98 computer to another Desktop PC / Tower PC <running Windows XP or newer> and copy the data this way.