I believe that you are getting Compatibility Mode and XP Mode mixed up here. A 64-bit operating system is a 64-bit operating system. Windows 7 can be purchased either in 32-bit or 64-bit versions, though most commonly it is now installed as 64-bit. Some 32-bit programs have no problem being installed in a 64-bit environment, but others just don't play nice and require a 32-bit OS. Flexi 8.1 is not supported on 64-bit OS, but it's not supported anymore period. I have heard of others running it in a 64-bit OS, just as Williams Signs has stated.
Windows XP Mode is an add-in that can be installed in the Professional and Ultimate versions of Windows 7 and simply acts as a virtual machine with Windows XP running for access to old applications that will not run on newer operating systems. This XP Mode ran in Windows Virtual PC which is a very simple and low-resource intensive virtualization utility that is rather limited in its capabilities and feature sets but pretty simple for people to figure out at least. There are many newer and better options out there now. Windows 8 Professional can likewise have Hyper-V installed, which is their enterprise level virtualization environment to run much more powerful and flexible virtual machines from Windows XP, Linux, and even Mac OSX. This is free for anyone running the Professional version of Windows 8. Personally, this is one of the greatest things I love about Windows 8. You can actually set up a fully virtual server system running on Windows 8 or Server 2008/2012 and move virtual machines back and forth with ease. What this means for small businesses is that if their primary server goes down, while they are running a Windows virtual machine, that VM can be copied over to any Windows 8 Professional computer in their network, turn on, and be up and going without hardly any downtime. No need for an expensive backup server or additional licensing.