Apart from the fact that the numbers just don't add up and you'd have to flow enormous amounts of seawater through the device, there are a couple of other problems:
- Breathing pure oxygen is fine at surface pressure, but it quickly becomes toxic when submerged
- You want the rest of your breathing air (21% oxygen or less, as you descend) to be made up of an inertial gas
- Lungs need to inhale and exhale to get the gas exchange in the alveoli to work, so you need a full lung volume of gas available at any time, not just the amount of oxygen required to run your body
- To get rid of CO2, you either have to release gas into the surrounding water, or scrub the CO2 using something such as soda lime
- Apart from the scrubber, you need to have these additional parts for it all to work:
1) some kind of counter-lung to allow for breathing movement
2) some kind of pressurized gas to increase the amount of gas in your lungs/counter-lung to compensate for the compression of it all at depth and to dilute the O2 content of the breathing gas
So, great idea. You have to lug a full rebreather system with you for it all to work, but luckily you can leave the 2 liter oxygen tank at home and use these fantastic gills instead - until the not-yet-invented next-generation battery powering the extremely powerful "Micro-Compressor" runs out of juice.
The only way this could work out to be something useful would be to hook up a major blood vessel to the device, allowing for gas exchange O2 CO2 between the water flow and the blood through the device, bypassing the lungs altogether. As an alternative, fill the lungs with a liquid (as in liquid breathing) and do the gas exchange between the breathing liquid and the water. Less messy that surgery.