**Alchemist Items have a rarity just like any other item**

It might not be listed in the Adventurer's Vault but all items in 4e were overhauled to have an [Item Rarity][1] of Common, Uncommon, and Rare. Common Items can be easily found and purchased. The item rarity rules can be found in the free, downloadable [Errata][2]. You can lookup an Item's rarity quite easily using the [D&D 4e Online Compendium][3]. To read the item description you would need an Insider account subscription, but you can search and see the results without a subscription and one of the columns is Rarity. 

Yes, anyone can purchase *Alchemist's fire*.

A quick search shows that Alchemist's Fire is common and thus they should be able to find and buy it. Use your judgement as a GM, a small rural village probably won't have it, but a bustling city should have it in stock somewhere. 


  [1]: http://archive.wizards.com/dnd/article.aspx?x=dnd/drfe/20100824
  [2]: http://archive.wizards.com/dnd/Article.aspx?x=dnd/updatesarchive
  [3]: http://www.wizards.com/dndinsider/compendium/database.aspx