You have the preferences set for two-sided reports (full duplex mode) in Kennel Connection under File, Printer Setup, Preferences. But Kennel Connection only prints one-sided reports.
In Kennel Connection, when you click on File, Printer Setup, the settings here don't matter because all this screen does is mirror that of your Windows printer screen and settings. You must have your preferences set through the Windows printer setup screen.
There are no settings in Kennel Connection itself to control your printer. It sends the print jobs to the printer and the printer handles the rest. Some printers read print jobs differently so it's possible this issue is due to the format of some reports and the way the printer reads them. Sometimes printers will read one job as separate print jobs; therefore, instead of printing front and back, it prints on separate sheets of paper.
Unfortunately there are no settings in Kennel Connection that can address this issue. Your printer's manufacturer may have a FAQ or support page that can give you guidance. Most of the time these issues can be resolved by going into Windows Control Panel, Devices & Printers, right mouse clicking on your printer, printer properties and setting the correct settings there. Whatever settings you set here, KC will use.