To be able to adjust the delay of your acquisition from your start trigger in DAQmx you should use the DAQmx Trigger property node. There are two values you would need to set in order to achieve this functionality: Start.Delay and Start.DelayUnits (See attached delaySettings.GIF and delaySettingsWhere.GIF for the location of the different options). By using a control for at least the Start.Delay, you will be able to change the delay from the front panel.
The Delay Units can be set to be Seconds, Ticks or Sample Clock Periods. The attached file shows how I used Seconds as my Delay units. You'll probably want to use Sample Clock Periods, and that will mean you'll need to do some arithmetic to get the millisecond accuracy. For example, if you have
a Sample Clock Rate of 1MHz, a user would need to enter in 1000 to get a millisecond delay. This also means that my previous response wasn't quite correct. Even though you don't need the microsecond accuracy, you could achieve a microsecond delay using the Trigger property node with a fast enough board.