No rifle can do that...it requires a combination of a rifle and a rifleman. In theory, there are any number of rifles capable of doing it; the crux of the problem is that more powerful cartridges capable of providing flatter trajectories that make it easier to hit a target at 1000 yds, will generally recoil heavily enough that they inhibit the ability to reacquire the target and fire for a sustained rate of one round every three seconds. To my knowledge, the feat has not yet been accomplished, but the challenge was issued by Jeff Cooper, who was amongst the most highly respected and accomplished gun writers, gun designers, and tactical trainers of the 20th century.
The Walther WA2000 I referenced in my previous post stands perhaps as good a chance of any rifle as being of the type used should the challenge ever be met...probably the biggest factor that would prevent it is the fact that so very few were ever made.
Thanks for providing that stuff.
Would something like 30.06 be a good cartridge in terms of as little recoil as possible, with giving as flat a trajectory as possible?