Withdraw action, passing into the Gauntlet, to hopefully reach the other end, and find a way to shut it off for everyone else (after all, the trap's makers probably would not have made a whole section of their dungeon impassable to themselves...). Could Kulkav's lingering glances at the process before the group left count as studying it? If so, then he gets +4 to these checks. If not, this has a good chance of getting messy...
So, for the Swinging Blades, he'll be taking a Jump check.
[roll0] (vs. DC 17)
For the Spear Trap, he'll also be taking a Jump check.
[roll1] (vs. DC 34)
*For the curious, Jump check breakdown:
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4 ranks in Jump, +8 from Strength, +4 from Barbarian speed, +10 from his Dragon Wings trait, and against the weapon-based traps, he gains an additional +4 from his tower shield.
For the Pit Trap, it is my hope that Kulkav can avoid the need for a check, or get an easier Strength check from his methodology (for reference, his strength is presently greater than a Hill Giant's, and his load is presently Light, so it's my hope that keeping himself in place via friction should be a simple task). Since he is Large when he rages, he has enough reach to apply force beyond both walls. However, in case checks are necessary,
[roll2]
please use this against either the normal DC or an easier Strength DC. His Str bonus is equal to his attack bonus, given the -1 from size (unless it's irrelevant for this purpose, in which case please add one more, and the shield can at least be used to protect against any impact, in which case add four more).
Next, Fireball trap. For this, Kulkav will Jump.
[roll3] (DC 18)
Same for the Chompers.
[roll4] (DC 19)
Finally, the most dangerous part of the process: the Buzz saws. For this, Kulkav will go with an attack roll.
[roll5] (DC 20)(+1 if size is irrelevant, +4 if his mental prep is sufficient for the trap)
Edit: BOO-YAH!