To make Kickoff Legacy application launcher taller, simply edit the file /usr/share/plasma/plasmoids/org.kde.plasma.kickofflegacy/contents/ui/FullRepresentation.qml and change the minimum height value from 34 to 50 or any other value that suits the monitor resolution.
Layout.minimumHeight: PlasmaCore.Units.gridUnit * 50
Reboot or logoff/login back to reload the application launcher with the new modified height.