The manual that came with my KX1200.1 calls for 1/0 GA power wire and the terminals are built to hold 1/0 GA. I asked about this awhile back. The gauge of the wire will depend on the length. You can get by with 4 GA from a distribution block to your amp if you're only gonna use 3-4 ft. of 4 GA to your amp, but you need at least 2 GA running from your battery to the dist. block. I finally decided upon a dist. block with two 1/0 GA inputs/outputs and four 4 GA inputs/outputs. I'll be running 1/0 GA to the dist. block into one input and I'll use the other to run the 1/0 GA to my KX1200.1. I'll be running 4 GA from the dist. block to my KX450.2.
Anyway, you definitely do not want to use 4 GA from your battery to that amp. You need 2 GA minimum for that length.
4AWG is good for up to 150A peak.. decreasing proportional to length.. so yeah I'd go 0 or 2AWG, then split to smaller at the amp if you wish, or pass through and stay that big to the amp and be able to go to a separate second amp off of the d-block later if you like 1/0 will give the upgradability.. you'll have current capacity to spare