Can we use java keystore in this case?
A Java keystore file could be used to share the key data, but you would need to password-protect this file to ensure other parties cannot read the key. So you've only changed the problem to how to securely share a password.
A common way to solve your original problem is to use asymmetric cryptography. By encrypting the AES key with a public key held by your recipient, you've ensured no others can read the key data. However, you will still need a method of determining that the public key corresponds to your intended recipient. For that, most people revert to a PKI of some description.
This is a broad subject area and worthy of some further reading on your part before you determine the correct approach for your use case.