Stainless steel contains fair amount of Cr. Cr is the main reason why stainless steels are "stainless".
I never tried this, but I think this is relatively safe (make sure you wear gloves, goggles, and lab coat; do not get the chemicals on your skin) so I'll try my best to answer the OP's question.
You could try partially dissolving stainless steel in acid (for example HCl 1 - 2M), take the water solution, and use some sort of chelating agent. Then you could try using NaOH (1 - 2 M?) to change the pH so that Fe(chelate) precipitates, leaving Cr in the water solution. Check the color and see if it is the supposed to be color of Cr(chelate). I believe this method can be quantitative as well.
I don't know what chelates should be used, so you need to look that up. HCl and NaOH can be bought by general consumers in my country.