You sadly can't seem to change the board size in KCheckers - you can change the board to 'simple-big' in the 'View' menu, but that does not make much difference. It may have last been updated in 2005, so is a real space for development.
You may want to try this - though it is designed for Ubuntu Touch, it is shown working in Ubuntu 13.04 (with a cursor... so I looks like it works on the Desktop Ubuntu as well.) - though I get this error when trying to open it:
wmobbs@whm2:~$ qmlscene --desktop_file_hint=/usr/share/applications/checkers.desktop /usr/share/checkers/checkers.qml
file:///usr/share/checkers/checkers.qml:49 ToolbarActions is not a type
I should do a bug report later.
If you are using 13.04, you may want to update it, as 13.04 is now End Of Life - example instructions here.