How to power my 12V Kinect from an 11.1V LiPo battery?
That Kinect USB supply is a strange beast :)

The most straightforward way is to do as you suggested.  That is:

Battery -> Inverter -> Kinect power supply -> Kinect.

You can use any convenient connector between the battery and the inverter.  If the inverter is already wired to a cigarette adapter then that would be a convenient choice.

However, this isn't very efficient.  Each time you convert power you lose some of it to inefficiencies.  You are taking the battery voltage (~11V DC), changing it to 120V AC, and then changing it again to 12V DC.  Let's say that each conversion is 85% efficient (which is reasonable).  0.85 x 0.85 = 72% efficiency.

So, here's how you calculate it:


The Kinect power supply is capable of outputting 1.08A @ 12V DC.  This is your worse-case consumption.  12 x 1.08 = 13W.
Now account for the inefficiencies. We already calculated 72% eff, based on earlier assumptions.  We need the battery to provide 13W / 0.72 = 17.8W.
Your battery is rated at 6.4 Amp-hours.  Multiplying by 11.1V (which doesn't account for actual battery discharge conditions) gives 71 Watt-hours.
So your battery can provide 71 W-h, and your system needs 17.8 W.  Divide it out, and you should get around 4 hours.


This is a rough number.  On one hand, the Kinect won't always draw full power. On the other hand, the converters might not be that efficient.  If they are both 80%, then the total efficiency changes to only 64%!



There are a few other things to consider.


How low do you expect the battery voltage to go before you consider it depleted?  Make sure your inverter can run that low.
How will you decide when to stop drawing down the battery?  You don't want to just run until something stops working :)
For 17.8W and 11V, the battery will need to supply 1.62A.  This is fine with your battery, but I've included it here for reference. Unless you have good reason, you generally want to keep your current to 0.5C (which in the case of your 6.4Ah battery, is 3.2A).




Finally, as you have mentioned in an edit, you are starting with DC and ending with DC.  Why go through all these conversions?

Two main reasons:


You don't need to modify / destroy your power adapter
Your battery isn't supplying the 12V needed by the Kinect.  You'd have to step up the voltage, which is a whole other design challenge.