Attic truss has a diagonal brace (red) linking all but outermost king posts (blue). I would like to flip the orientation so that instead of starting at bottom at one end and ending at the top, it would start at the top and end at the bottom. Everything else would remain as is.
Does the orientation of the brace matter?
If there's only the one, no, it doesn't matter.
If (your drawing, being partial, leaves the complete framing picture unclear) there are a pair of them in the structure such that the pair form an X brace, you'd have to switch both.
Or, if your description is a bit off, the orientation can matter (I have similar braces at each end of my roof, which are indeed specified to run from the peak at the end truss, but they don't go the full length of my roof, which is what your text says this does. Those would not work quite the same inverted. If this does, as you say, go the full length, inverting it would make no difference.)
Ecernwal's right, but chances are that brace is doing nothing. That sort of thing is often installed during construction to stabilize framing, but once the roof is sheathed there's no way the assembly can lean in the manner that such a brace would prevent.
I've installed many engineered truss systems, and never is there a brace specified that's askew like that. They're always aligned with the ridge and tight to the center struts, with specific nailing schedules to each truss. No truss designer will specify a brace fastened akimbo and only at the ends.
Every engineered truss package comes with clearly detailed bracing schedules. There are no standard requirements. They don't all have these. There's really only one way to know for sure, and that's by consulting either the original paperwork or an engineer.
So yes, you can relocate that brace, but when you do, nail it flat to the vertical truss webs on each truss with two 12d nails or larger so it's actually doing something.
Leave it alone. According to the SBCA's Guide to Good Practice for Handling and Installing Bracing of Metal Plate Connected Wood Trusses,
Web [permanent individual truss member restraint] and diagonal braces used for installation stability purposes and installed at the locations specified for [permanent building stability bracing] can become part of the [permanent building stability bracing] system.
Your diagonal braces are therefore part of the "permanent building stability bracing system." An inspector should have demanded removal of the diagonal braces if that was not the case. The truss design drawings would have specified admissible locations and configurations (admissible yet probably not necessary), but I doubt that you'll find any trace of those documents.
In reality I suspect that designing these braces for "permanent building stability" actually involves verifying that they're not too stiff. If they were too stiff, then they could damage the structure before roof sheathing deflects sufficiently to do the actual resisting. (Put more succinctly, "I suspect that @isherwood is right.") Unfortunately that's just speculation on my part.
Here's the way I look at the use of a brace.
This shows a typical gabled end roof, like you find on many ranchers:
Here's the same roof structure looking at it from the side.
Now when the wind blows onto gabled end of the roof, the flat gable wants to collapse, or pivot about its base. The diagonal brace helps to prevent that from happening.
Without the brace, the roof wants to collapse, or parallelogram, like this:
