If you do the Tamiya 1/350 kit, you'll need to purchase the Tom's Modelworks Square Bridge Conversion set if you want to model the Kidd.
The Tamiya kit is Fletcher in her as-commissioned rig. Round bridge, forward 20mm guns, etc...
Kidd carries a square bridge, MK I 40mm mounts forward, MK II 40mm mounts midships, her forward torpedo tubes have been landed in favor of a platform for the MK 52 Fire Control Directors for the quad 40s. Her 20mm mounts are all twins with MK 14 reflector sights, not the early MK 5 ring sites.
With regards to decals of the Kidd's funnel emblem, no one does one to my knowledge, but you can probably find an online sample, or talk to the ship staff, and print your own decals.
Jeff Herne