I'm assuming you're referring to hand embroidery, not machine embroidery (on a sewing machine) which is more difficult and some machine embroidery uses a special machine.
Since many "jackets" are made from thick sturdy materials, they might be *tough* to get a needle through, and more so if the design you choose requires a lot of stitches (pushing in and out of the fabric many times) for that pattern/design.
Just learning to embroider though on its own isn't very difficult, and a bit less even since you're already familiar with doing hand sewing of any kind. In fact, it's lots more fun and more interesting than cross-stitch or just regular hand sewing.
So sure, you or anyone could learn to embroider in a month, or even in a day, but there are a lot of different embroidery stitches you might or might not need to learn:
The pattern/design you choose (or create yourself) might have only a few basic embroidery stitches or it might have a lot of different stitches and some can be a little more difficult or just time-consuming than others.
Also, the design/pattern you use might cover a lot of an area which would take more time than one that didn't cover a whole area fairly solidly with stitches (although some stitches can cover a lot of area just because each stitch is long). I'm referring there to the area you've chosen to embroider, perhaps an area 5x5"...it might have embroidery that covers the whole area rather solidly, or have only stitches here and there, etc.
The only things about embroidery I found difficult at all or took any time to learn were just how to hold the fabric (or embroidery hoop if you use one, and how tight to stretch it), learning each new stitch (most not difficult though), and then just practicing so the lines and margins would be even or the stitch done exactly right, etc.
Check out some of these links for "how to embroider a jacket by hand" (and if you'd be doing machine embroidery substitute the word "machine"), but would be best to add the name of the fabric (like denim, linen, cotton, etc) of the jacket you're planning to work on to the end of each url:
To learn the stitches and general tips for hand embroidering, check out some links like these (some are videos, some are websites with diagrams and tips):
(++ see links just below)