Is there any way to have a flash drive encrypted and it will only open with one computer that has the key in it?
Install a program like PGP, and save your public and private keys to your hard drive - specifically in your own login account. Encrypt the drive. When you try to decrypt it, it will require your private key. Don't copy the keys to any other source. Many dual-key encryption methods are good for this purpose.
For the PGP example, there are whole disk versions of PHP that use key and passphrase.
More info on that topic can be found here:
"PGP Whole Disk Encryption can encrypt the thumb drive so that it is only usable on computers with the proper keys." http://symantec.com/connect/blogs/doing-more-pgp-whole-disk-encryption