The way you have connected the sensor board is wrong. First, the sensor board's 0V rail needs to be connected to the 0V rail of the acquisition device. Second the board requires a power supply voltage of 6V +/- 0.1V to drive the hot wire inside the sensor, and the sensor draws about 200 mA from this rail, so the source of this voltage must be able to supply that much current comfortably.
You can provide the 6.0V DC voltage from an external power supply, or you may be able to use the data acquisition device's +15V DC output with a regulator. There are two types of regulators: linear and switching. Each has advantages and disadvantages.
A linear regulator requires slightly more input current than its output current, so your +15V supply would need to be rated for at least 250 mA. The regulator may get quite hot, depending on the amount of voltage that's dropped across it; operating from +15V it will drop 9V and at 0.2A will dissipate 1.8 watts. It will need a smallish heatsink. It will produce a clean 6V supply to the sensor module. A suitable device is the 7806:
http://www.digikey.com/product-detail/en/MC7806CTG/MC7806CTGOS-ND/1481226
Switching regulators are available through eBay as fully assembled PCBs. They boost current as they reduce voltage, so you would only need about 100 mA from the +15V DC supply. Also they are quite efficient so you would not need a heatsink. However, they generate significant noise, which could interfere with the accuracy of the sensor board. You could add external components (inductors and capacitors) to reduce the noise, but I can't say whether it would be a problem or not.
If you have any more specific questions, please ask.