I'm not enamoured with the final effect of the rust in the OP. Looks much better in the WiP picture. At a guess I would say on the axe the rust has been stippled on and for other sections a wash used.
For clarity, stippling is where you take a stiff bristled brush, get some paint on it but remove most (do not remove as much as if you were drybrushing) and then vertically jabbing at the area you want the paint which, because of the stiff bristles, gets a dotted effect.
Washing is where you take your paint, water it down a lot before applying it to the model and this way it pools more to the recesses.
For the axe:
Paint bolt gun metal.
Stipple on bestial brown.
Stipple on vermin brown.
Streak chain mail/mithril silver onto the blade and highlight as wished. Do this in areas that would see the most use or abrasion as they would be the most highly polished and rust that forms would be removed through use (fun, huh?)
Stipple on vermin mixed with blazing orange.
For other areas: (I suggest doing a google image search on rust to get some reference images)
Paint model as normal, highlighting to satisfactory standards ignorant of rust.
Paint areas where you want rust with bestial brown.
Wash these areas with vermin brown.
Wash parts of these with a mix of vermin brown and blazing orange.
It looks to me like solitaire took his mix right up to straight blazing orange, which I consider too bright for an aesthetically pleasing rust.
Use your own discretion with how to shade the colours, how heavy to make particular stages etc. If you want it darker, mix the bestial brown toward scorched brown with a little blazing orange (to maintain the "oranged" look you get with rusts). If you want it lighter use it closer to blazing orange for the finished colour.
Because rust doesn't oxidise completely evenly and you get patchy bright areas that are not "logical" to the way you'd highlight a model (in the same way that painting flame does not follow standard logic) I cannot emphasise enough he importance of finding some good references that show how much rust you want and using them while painting. In my opinion the rust on the Death Guard is too bright and too clean, especially given the setting, and while excellent can be improved upon if you use reference to see how the rust would actually settle. These
photos look like an extremely good reference.