I’ve be researching about this, too. Seems there’s not full support yet in Inskcape (I guess you will need for vector based art for t-shirts, logos, etc) for printing workflows, though a lot of people, mostly in the open source world, does use it. A method that seems (there will be allways issues to be aware of) to work is : Make your vectors in Inkshape, which is quite advanced for that. Even your color, fills. Better don’t use “effects” , but mainly pure solid gradients, better if not transparency, and try also to convert fonts to outlines. Then export to Scribus, as seems it has both actual good export for printing workflows, and a preview of the colors being converted. Oh, don’t go to a line width less than 0.5 points, and don’t do detail super small if aiming to vector based cmyk printing tshirts in those kind of companies. Try to close all shapes, and don’t leave rubbish isolated points or lines. These places do hate that.
The main issue is that the packages need to support cmyk ICC profiles , mostly the main ones used by most companies (usually 2 ) .IMHO this as first step, then add the pantones, if that’s possible legally. But achieving the profiles matter is key. And you will usually give your EPS or PDF file to the printing company with the embedded ICC profile they actually use, reducing this way the possibility of errors.
I keep an eye though (mostly the Windows build, not released yet. I can load virtually a linux, which I like too, but wouldn’t fit my workflow) in SK1 project, (a kind of Illustrator package, open source) as seems to be really targetting professional printing ouput.
Of course, GIMP with dunno if certain CMYK plugin seems to work for quite some people. For the non vector based works. Outputs, I mean. You can allways export from Inkscape a vector logo and import in Gimp with a huge resolution, then print cmyk, etc, not the way to go, imho, for logos, vectors stuff. Many companies will want the actual vectors…many do not, specially the non huge companies . I know there are though, a lot of customers and companies that are ok if you provide them with a 300dpi raster work, in a big enough size of inches (in the end, all are pixels, tho ) with all versions, and variants needed for the usual company projects.