I have just recently completed some reports under Joomla so thought I would write down how I did it for others.
First, get a copy of Koolreports. Create a directory under JPATH_ROOT/libraries called koolreport. Unzip your koolreport into this directory.
Second, get a copy of the JUMI extension and install it. Get this from the Joomla Extensions Directory.
Third, create a directory somewhere under JPATH_ROOT for your koolreports reports. Under this directory create a new directory for each report and place your koolreport index.php and other related files in their respective directory. Remember to include the koolreports autoload at the top of your index.php, like this: require_once(JPATH_LIBRARIES.'/koolreport/autoload.php');
Fourth, create a new JUMI app. In the custom php section add the <?php followed by an include statement to include the appropriate index.php of the report you want. Or, you can point the pathname to the index.php file.
Fifth, create a menu of type JUMI and select the app you just created.
Now you can access the Koolreport from your Joomla menu system.