One PC has program so old the installation "disks" are 2 floppies! It is Windows Family Tree Maker. My Mom has new PC (Windows 8) and wants to transfer all the data and program. Can I do this using a flash drive?

I think your best bet is to buy the newest version, do an export from the old PC and import the files into the program on the new PC. Assuming it is this product: Family Tree Maker by Ancestry.com - The #1 Selling Family Tree Program