I don't have any experience working with LabView or LINX so I don't know how it works but to read a value from the ADC Pi Plus you have to first send a command byte to the I2C address for the ADC chip and then read either three or four bytes depending on what bit rate you have selected. The three or four bytes have to be combined together into a single value which can be converted into a number. You don't have to send any commands when you first power up the ADC.
The ADC Pi Plus uses the Microchip MCP3424 ADC chip, the datasheet for the chip can be found here. The details on what you need to put in the command byte can be found on page 18 and how to read back the values is on page 22. Once you have send a command byte you will need to keep reading from the ADC until the ready bit goes goes low which tells you that the data conversion has been done and the value is ready to read.
To get an idea of what code you will need to read the values from the ADC it may be worth having a look at our python library. The read_raw function contains the code for reading a raw value from the ADC chip and the read_voltage function converts that raw number into a voltage based of the gain and bit rate settings.