I just did a quick google search and it looks like the mantles are definitely available. Just in case this wasn't clear, the mantle for a kerosene lamp refers to the glass tube that goes over the wick, but Aladdin lamps have two different "mantles". One is a glass tube. The other functions more like a wick. It starts out as a little net bag like this:
Once you start using it the net turns into a structure made of ash, which glows when the lamp is lit. If the flame is turned up too high a part of the net will turn black and not glow. Then you need to turn down the flame for a while and the black spot will go away. It's quite tricky to get it at just the right level to produce a good amount of light but not damage the mantle. The mantle is also fragile once it has become ash. If you knock the lamp, a part of the mantle might tear. I've never looked any of this up as an adult; I'm giving you my childhood practical understanding of it. A more technical understanding might be more useful. I personally don't like using the Aladdin, because it is so fussy. But it does make a nice light. You need a glass or paper shade which goes around the glass mantle because it is too bright to look at.
My mom has had her Aladdin lamps for decades. I don't know where she got them or how much she paid, but they certainly last.