Since fluxbox is designed to be lightweight, it doesn't natively support icons on the desktop. However, there is add-on called fbdesk
that allows you to have icons on your fluxbox desktop.
If the slit is annoying you, you might want to try using tabs. Personally, I think it is one of the nicest features of fluxbox. If you are using the stable version, the tabs stick up above the top bar of each application window. Just click with both mouse buttons on the tab and drag one tab on top of another. The windows will re-size and you can flip from one to the other just by clicking on the tab. In the development versions of fluxbox (which I highly recommend), the tab has been integrated into the top bar of the window. If you do the 2-button click on that bar, it behaves exactly like the earlier tabs.