If you are the art I'll be the brush.
"The" is used for definite and specific things, so shouldn't it be
If you are an art I'll be the brush,
or
If you are an art I'll be a brush,
or
If you are an art I'll be your brush?
If you are the art I'll be the brush.
"The" is used for definite and specific things, so shouldn't it be
If you are an art I'll be the brush,
or
If you are an art I'll be a brush,
or
If you are an art I'll be your brush?
The first point is that you can't use "an art" in that way - the phrase does exist, but it has special meanings, either "an artistic field of activity" (such as painting or sculpture) or "a special skill" (as in "there is an art to writing"). For the sense you mean, you would need "a piece of art" or "an artwork".
But, to address your question: this is poetic language*, which doesn't necessarily follow the usual rules of syntax. In ordinary speech, I can just about imagine somebody saying "If you're a painting, I'm a brush" (though it's not very likely). But this form "If you're the painting, I'm the brush" is definitely poetic. In the love duet in Iolanthe, W. S. Gilbert wrote:
Thou the tree, and I the flower;
Thou the idol, I the throng -
Thou the day and I the hour -
Thou the singer; I the song!
I suppose you can justify it by saying something like "In the imaginary scene that I am referring to, you are the art and I'll be the brush", where the definite article is identifying the things supposed to be there in the imaginary scene. But I think you're better just accepting that it is a poetic form of words.
(Actually, now I think of it, the use of the art in this way to mean the painting that is being worked on is poetic as well, and wouldn't normally happen).
Edit: *FumbleFingers points out that this is effectively a poetic idiom, where the definite article is normal.
I like Colin Fine's answer, but the way the definite article works in a "you be the X and I'll be the Y" construction is actually quite simple. The definite article isn't poetic. It's the particular pairings that are poetic in the W. S. Gilbert lyric.
The definite article identifies the nouns as the ones we expect to be there in a known or familiar duo.
You are the salt and I am the pepper.
You be the cat. I'll be the fiddle.
If you're the hammer, I'm the nail.
When my son was little there was a TV show called Flipper (in reruns), about a smart dolphin, sort of a seagoing Lassie. There was a father who was a game warden in the Florida Everglades, his two sons, and the dolphin. One of the sons was named "Bud". My son wanted me to play a Flipper game with him one day, pretending to have similar lives and concerns. He said You be the dad and I'll be the Bud.