Are you looking to refinish or just touch up your frame?

Paint codes vary from manufacturer to manufacturer, and not all have cross-references to the others' codes. And yes, this is probably at least a two-stage paint process. Most paint jobbers have optical color matching devices that might get you acceptably close. If they don't, they'll have books with sprayouts that you can use to compare colors. But their sprayouts might not have the right metallic or pearl or be just a little light or dark or whatever. That's why experienced painters match by eye, using their own sprayouts for fine-tuning. In the case of a multi-stage process, this can get complicated, because older paints' nuances can be difficult to replicate.

There's no way to match paint colors on computer screens or photographs either. Colors are produced by the devices and decoded by our brains differently from how paint is.

Sorry, no easy way around this. If you want a spot-on match you will have to have an experienced painter with a mixing system at hand decode what's on there, then take the time to replicate it. There's a real art to it.