Something smells burning in the kitchen
is not idiomatic in American English.
The problem is that "smell" is not just a linking verb. It is also a transitive verb.
I smell smoke in the kitchen
does not mean that my odor changes when I enter the kitchen. As Samuel Johnson once said when a lady told him that he smelled, "No, madame, you smell; I stink."
It is true that we can use participles as adjectives, but it is also true that we can use present participles as nouns.
Something smelled burning"
creates ambiguity because it is not clear whether something (a dog for example) sensed the odor of some other thing being burned or something is emitting such an odor.
Something smells as though it is burning
is perfectly clear that "smell" is not being used transitively.
If we change to a perfect participle, which cannot typically be used as a noun, the ambiguity disappears, and the abbreviated form becomes idiomatic.
Something smelled burnt.
Because "burnt" is not a noun, it is clear that "smell" is not transitive.