SHA256(RsaPrivateKey) == AES key?
First of all, the usual way to do this is to generate a new random AES key and then wrap it with the public key. Generally you don't encrypt with the private key at all.

Yes, SHA-256 is a one way hash so you can do this. The problem is that you would still need to encrypt with a public key to let the other party know the AES key (unless you use the key to encrypt for yourself, of course).

There are however a few pitfalls:


the private key needs to be encoded as bytes, and not all encodings are canonical; i.e. you could use different encodings for the same private key. If this ever happens in your scheme you would not be able to generate the same AES key;
you'd need a separate input - e.g. a counter (nonce) - if you want to generate more keys;
SHA-256 is not a KDF, you could use HKDF instead (which just requires a hash function to work).
Sometimes hashes over private keys are used as key identifiers. You must make sure that this is not the case. For RSA however the key identifier is usually generated by a hash just over the public modulus.
You'd forgo the option to store the private key within a security module, as direct access to the components that make up the private key would likely not be available.


The biggest question that you should ask yourself is this: why do you need an AES key for encryption at the location of the private key. That's a strange use case.