I currently have a VI that controls the discharge of a battery cell via several GPIB devices. These devices need to be fairly well timed for everything to work right and the discharge to be successful. I also need to acquire 15 seconds of data during the discharge like cell voltage and current and a few other voltage readings.
I currently use an external device to acquire the data and wish to switch to a PCI-6143 card that happens to be installed in the computer I'm using. I have never actually used a card for data acquisition. I've always used a secondary external device.
I can set up the card to get all the data I need, that is not the problem.
The problem is that I cannot figure out how to integrate the data acquisition into my VI and get it to run correctly. Currently if I start the 6143 acquiring its data my VI waits until it has it all before continuing on to the next frame.
Is there a way to trigger this thing in one frame and then continue on with the rest of my VI while it's recording the data?

Put the acquisition into a separate loop. Use a notifier to trigger the acquisition, and a queue or similar to pass the data back to your main loop when the acquisition completes.

You did not provide a screenshot of your code or any VIs so I have to guess what's going wrong.
It guess you should use the lower level DaqMx VIs instead of one VI that starts the daq tasks and fetches 15 seconds of data.

Did you have a look at the LabVIEW daqmx analog input examples, there must be an example that gives you a hint how to handle this task?