I searched the Keithley website and did find a GPIB driver for this instrument. Also, LabVIEW comes with Data Logger examples (Help >> Examples >> I/O Interfaces >> Data Acquisition). You would have to write a VI that would call the instrument driver and data logger simultanously.
One suggestion for synchronizing the the signal collection would be to send one channel of data through both the DMM and the DAQ card -- sort of a reference channel. Then, after data collection is over, you could compare the reference channel data from both the DMM and the DAQ card. If necessary, you could 're-allign' the datapoints...