The 340 Gibbs is just a 338/06 "Improved", by reducing taper, reducing neck length, and blowing out the shoulder. You are gaining at most about 10% more case capacity, so should expect no more than 2.5% more muzzle velocity over the 338/06 if you keep pressures the same, i.e. compare apples to apples.
I'd start with published max 338/06 loads and increase by 1/2 gr increments. Your starting MV will be less than for the 338/06 due to the lower pressures created within the larger case, but will eventually meet, then exceed 338/06 velocities. Once your chrony shows 2.5% more velocity than published as max for the 338/06, that is your max for the 340 Gibbs. For example;
Hodgdon says a max load for a 200gr bullet is 59.5 grs of BL-C(2) and gives a MV of 2850 fps. Start with 59.5 grs of BL-C(2) and once your MV reaches 2925 fps (2850 + 2.5%) you stop.
Of course with Gibbs cartridges, most users ignore pressure and look for "pressure signs" such as loose primers, sticking bolt, etc. That's a crap shoot I avoid.