As has been pointed out in comments, the brain can certainly affect gene expression; but so can anything in our bodies, because the blood stream is super good at carrying stuff around the body to wreak havoc.
But I'm going to take a somewhat uncharitable view of this question1; and assume that what you are asking about is high-level mental processes affecting gene expression throughout the body, which is not a thing that happens.
The basic concept to bring forwards here is that the brain is hell-a layered. The brain is an extremely complicated organ, and while it's not a complete mystery, it's not an organ that we generally can be said to understand, at least not on the level that we can be said to understand in major terms how, say, the liver, kidney or spleen works.
What we do know is this: The brain forms a massive network of neurons; the shape of which informs our personality, memory and cognitive functions. Even our simplest thoughts involve, by necessity, thousands of neurons, and anything more complicated than 'Fire!' involves tens, hundreds or thousands of thousands (millions) of neurons.
At the same time, it's important to understand that our brain does a lot of things that we're not directly cognisant of. For one, our brain controls our breathing. As you're reading this, you'll discover that you take control of your breath, but also that you haven't done so for several hours at the very least, and maybe not for days or weeks, and you haven't died from hypoxia yet. Our brains do these kinds of things all the time, and we hardly ever notice.
Genetics are a very, very, very low-level thing. Way lower of a level than mere breathing, genetics is the engine that drives decision making at a cellular level; which is so far removed from consciousness that it's hardly imaginable.
And this is where layering really comes into play: While recent research indicates that brain cells have hijacked DNA replication techniques to store memories, most of our actual thoughts exist only on levels that are so much higher than the nuts-and-bolts of our brains that the physical structure of our brains don't even come into play.
Essentially, thought as we understand it doesn't exist within individual neurons, but only within the relationship between neurons. When it comes to cognitive or metacognitive processes, things like genetics becomes an implementation detail isolated from the higher-level system as a whole. The underlying physical structures can affect gene expression, but do so not as a response to thoughts or subconscious desires, since these don't exist in the individual neurons; but as a response to primal needs like "more sugar for the brain!" or "more oxygen for the brain!" or "more protein for the brain!".
In other words: While the (sub)conscious mind can affect gene expression, it does so in terms of resource management, not in terms of how body tissues act, because the mind as it is has no physical concept of bodily function.
1: Uncharitable, yes, but it does make the question more illuminating and interesting, IMHO.