One thing about dying it yourself, you have be ready to give up the item in case things don't work out - especially if you drastically change colors. So if you were going to toss the jacket, then you might want to give it a try.
The dyes only take on natural fabric. So if the jacket is 100% cotton, it should take. If the thread is synthetic, then the dye won't take. The same applies to the lining - although some dye might stick to the lining. It looks like the hardwear is metal, so that won't take the dye either.
One of the issues I see, is that you need a lot of stuff. That is why it is usually only worth doing it yourself if you do a bunch of items. You will need dye (of course), soda ash, and synthropol at a minimum.
If you are still game to try it, here is more information. I recommend using Dharma Fiber Reactive Procion Dyes. Below is a link to Dharma's page. Don't get scared away by the weird and wild samples, you are not making rainbow tie dyes, you will be tub dying (in a plastic or metal tub) one color. (The color lasts. I tried to bleach a dyed shirt and it wouldn't lighten.) There is also a lot of helpful information on their web page.
http://www.dharmatrading.com/h.....=dyes.html
Let us know what you think you will do. What color are you thinking of?