Not sure if you’re employed with Starbucks yet but if not, that’s step one. Also this is assuming you’re American trying to move abroad.

Step two: work for the company for a couple of months, and try to get promoted to supervisor until you’re in good standing with the district manager.

Step two point five: use the internal hiring system to search at where you have opportunities abroad, and think about where exactly you are hoping to go.
Step three: talk to your store manager and district manager and see what help you can get getting transferred to (wherever abroad).

This is where I run out of experience except for knowing these handful of facts:

1. To get a work visa, I think you need to have the work first before you get your work visa. Some people get the job on a travel visa and then apply for their work visa but this is safer, more secure, less expensive and less stressful getting the transfer first, then applying for your work visa.
This is how I understand it works with European countries with Americans, Asian systems of acquiring visas are more difficult and otherwise more unknown to me.

2. European Starbucks don’t always post through the internal means so it is necessary for you to get help from corporate to expend all means available to you (if they’re a good sm/dm/rd ) for acquiring a good position abroad.

3. In most of Europe, you are required to speak at a b2 level on the Common European framework of reference for languages (CEFR) for which ever language it is so this should be secured and tested before you try for a move abroad.

3. I apologize that my knowledge is exclusively European but I reckon you’d have the best luck in England or the Netherlands.

I hope any of this is remotely helpful.