Depends what was burned. Wood ash can be used to 'sweeten' the soil. Petroleum & synthetic ash is toxic. Ashes from dead animals can spread the lethal anthrax bacteria. Anthrax spores can remain viable in the soil for decades. Be careful!

Keep wood ash off raspberry canes though. if what you're burning is garden rubbish it can go on the compost heap too.

I don't see an 'incinerator' as being a wood burner, more like coal at the best. It needs to go into the rubbish bin.

Both fuel and fodder for your incinerator should be kept out of the garden, just to play it safe.

Having said all that if you are just burning wood you can use the wood ash in the garden or compost as long as it has not been treated with preservative.