Welcome to the club and congrats! You'll love your '02 Avalanche and you made a wise decision in a used vehicle. Now for the bad news, the "Tornado Fuel Saver" is pure 100% snake oil. Junk, doesn't do what it says, a waste of money, ain't happening, zero benefit, get your money back, thank you for playing, refuse delivery.
If you want to squeeze extra MPG out of your Avalanche there is only one way to do it and get measurable, guaranteed results:
1) By quality gas. Gasoline with 10% ethanol content is going to hurt your MPG.
2) Go with synthetic oil instead of dino oil. You can get a small, but measurable increase in MPG with the change that adds up over the miles.
3) Drive on the highway at 60 MPH. The Avalanche looses about 1/2 to 1 MPG for every 5 MPH you add over 60 MPH, depending on road and traffic conditions hitting a basement of around 15 MPG highway.
4) Use rolling momentum. Take your time and brake long, that way if the traffic is moving again you don't need as much whopf to get back up to speed.
5) Nice steady starts. Don't mash the pedal, actually considering WOT is only about 85% of capacity and torque control will rob you of acceleration standing on the gas pedal just makes noise and burns gas. Smooth acceleration is rewarded with more grumpf off the line for less MPG.
6) At highway speed run windows closed, back window in place, etc. etc. etc. I've found over the summer that having everything opened up cuts around 3/4 MPG of of the Avalanche.
7) Properly inflated and rotated tires. Common sense but if you reduce rolling resistance you get better MPG.
That's about it. You can expect anywhere from 11 to 14 city and 16 to 20 highway depending on a ton of factors to long to list here. Me personally, I get "textbook" mileage out of my Avalanche, around 12.75 to 13.25 city, 15 to 15.5 combined, and 17 to 18 highway.