Can you put Fire Aspect on an axe?
No. You can't put Fire Aspect on an axe in Bedrock 26.60, not even with an anvil.
Why not
Fire Aspect is not on the axe's list. Here is what an axe can take instead: Curse of Vanishing, Sharpness, Smite, Bane of Arthropods, Fortune, Silk Touch, Efficiency, Unbreaking, Mending.
What that means in practice
Fire Aspect goes on sword, spear and mace. The axe's list is all tool and damage enchantments instead: Sharpness, Smite, Bane of Arthropods, Fortune, Silk Touch, Efficiency, Unbreaking and Mending. So no anvil or table will put fire on an axe.
What to use instead
Axes can't take Fire Aspect in Minecraft. For burning hits, put Fire Aspect on a sword, spear or mace instead. On the axe, Sharpness is the enchantment that adds damage. On a fresh axe, Sharpness V costs 5 levels as a book.
Fire Aspect II on a sword is the closest match. It sets mobs alight, and a burning mob keeps taking damage after the hit. Many players carry both: the axe for heavy hits, the sword for cooked drops.
See Fire Aspect and Sharpness, or the full axe build.
Why the game says no
Fire Aspect only goes on sword, spear and mace. An axe is not on that list. That matters because Bedrock checks a built-in list of items for each enchantment. So the anvil gives no result, and the enchanting table never offers it.
No survival trick changes that. Combining two items, renaming or using a grindstone first all leave the list the same.
The best axe build instead
So a max axe has Sharpness V, Fortune III, Efficiency V, Unbreaking III and Mending. In the cheapest order it costs 32 levels over 5 anvil steps, and no step goes above 11. Open it in the calculator.
The best axe enchantments page explains every book, and the axe enchant order shows each anvil step.
Where Fire Aspect goes
- Fire Aspect goes on sword, spear and mace. Books on an anvil work on all of them. Related questions: Fire Aspect on mace, Fire Aspect on bow.
Commands and creative mode
The /enchant command refuses too, because an axe can't take Fire Aspect. Bedrock's /give can't add enchantments, so there is no way around it. The command generator writes the right syntax for your edition.
Java and Bedrock
As far as the item list goes, the answer is also the same in Java and Bedrock. The anvil differs, though: Bedrock only charges for the levels a book adds. This page follows Bedrock 26.60.
About Fire Aspect
Fire Aspect sets the mob you hit on fire. Burning mobs take extra damage over time and drop cooked food.
Fire Aspect has a max level of II. If you need a book, you can get it from the enchanting table, librarian villagers and enchanted loot from fishing and chests. Before you buy, read everything about Fire Aspect, including what each level does.
What else an axe can take
Instead, an axe can take Sharpness, Smite, Bane of Arthropods, Fortune, Silk Touch, Efficiency, Unbreaking and Mending. Then the best axe enchantments page ranks them and gives the max build.
Related questions: Sharpness on axe, Looting on axe, Smite on axe, Efficiency on axe, Knockback on axe.
Questions
Can you put Fire Aspect on an axe?
No. You can't put Fire Aspect on an axe in Bedrock 26.60, not even with an anvil.
What else can Fire Aspect go on?
sword, spear and mace.
How do I set mobs on fire with an axe?
You can't with an enchantment. Use a Fire Aspect sword, spear or mace, or a Flame bow.
Can an axe get Fire Aspect from an enchanting table or a villager?
No. The enchanting table only offers enchantments an item supports. A villager's Fire Aspect book still can't go on an axe, because the anvil checks the same list.