How can this be done so that for each system date timestamp I get the output of both the above commands?

I'm not sure I understand your question.

If you want to get the commands to run in the background, just add a '\&' at the end of the system command:(AIX/Unix/Linux)

system("date >> $vmstatOut \&");
system("vmstat 2 2 >> $vmstatOut \&");
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if you want get the results ever minute, put a 'sleep' command or run the script from cron.

Good Luck!