Maximum Current Draw on Vin Pin

You can look at the schematic for the Uno to see for yourself.

Looking at that, you can identify the power pins (top right) and see that the Vin pin comes straight from Vin, without going through the MCU or any other chip. Then, if you look towards the top you can see that the only thing separating Vin from the power supply is a single diode.

In short, there is nothing on the Uno that would limit the current draw of Vin. The only consideration is that you don't draw so much current that the voltage drops. This could cause the Arduino to reset (which is probably undesirable). So just limit your current to what your power supply can handle.

Edit: As stated in comments, the diode and trace width are other limiting factors. The diode is rated at 1 amp and the board traces can't handle much above 2 amp.

The Vin pin's maximum current is generally limited by the reverse protection diode, which is rated for 1A.

While you didn't ask this question, you should keep in mind that those small rectangular 9V batteries are very lousy when it comes to current capacity. They are only designed to provide small amounts of current, <30mA. The Arduino board itself draws almost 50mA.

Well... learned this the hard way. Max 1A