Old used tires are better than free, they are innoculous...they're eye sores or not noticed as assets.
Once they start burning, you don't need more fuel to keep tha fire going, simply toss more on top of the others. Spike nails can be stuck throught the tires so they'll remain, with hopefully enough pointing in convenient directions to continue to be a deterrent.
Focusing on the tire aspect of the briefing specifically, the uses of burning tires are numerous and they can be used in conjunction with many other devices, assets and techniques:
The best thing about burning tires is you can deny and/or canalize your enemy.
Burning tires provide a visual and foul smelling warning system of where the action is occurring.
If you're the side burning the tires, there's a psychological effect on both sides. Nothing shows chaos and violence like a city with burning tires in the street. Like battle horns and bugles, you're owning the air. You own that street.
Enough burning tires on a still day will affect low flying helicopters. They can affect some night vision as well and do some interesting masking of FLIR if there's enough fires, enough heat.
One burning tire can make something as large as an arena unusable for the duration of the burn and long afterwards.
Burning tires, being long burning can ignite/damage some things that faster burning fires like molotovs can't as readily ignite. (I forgot what specifically. Love it if someone knows.)
Burning tires are primarily a deterrent to wheeled vehicles directly, and to infantry and armor who don't wish to move through dense heavy smoke not knowing what's on the other side.
Rolling,burning tires can disrupt traffic, cause panic and be used against hardened positions. Burning, rolling tires can break up a mass attack.
Burning tires placed upwind of a hardened position can drive defenders out, prevent the use of openings for return fire, and can mask an attack.
A two-fer:

Set that off and even an M1A1 ain't getting through for days:

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They a total PITA to put out once going good. I've never personally used them for anything like above, but I have been around and participated in burning tires (and other junk) when I was younger. Hot burning fire and nasty black smoke......