The USS Tingey (DD-539) was a Fletcher-class destroyer. She was originally launched in 1943, served until 1946, recommisisoned again in 1951 and served until 1963.
http://www.navsource.org/archives/05/539.htm
When was your Grandfather on her? There is not a Korea/post-Korea Fletcher kit in 1:350 scale. The closest you can get for that is the Skywave USS Callaghan in 1:700 scale. It includes various bridge configurations as well as weapon & radar fits.
There is not a off-the-shelf kit in 1:350 scale styrene model of a WWII square-bridge Fletcher. The Tamiya offering is a round bridge (i.e. early variant).
Tom's Modelworks offers a conversion kit to convert the round-bridge to square-bridge. Besides the bridge it includes various gun & weapon fits. Call, it may be out of production.
http://www.tomsmodelworks.com/default.asp
Yankee Modelworks makes some very nice resin & brass square-bridge Fletchers .
Their USS Johnston is good
http://yankeemodelworks.com/kits.htm
If you want to go larger, Iron Shipwright offers a 1:192 scale resin & brass Fletcher
http://www.commanderseries.com/pages/Fletcher.html
I'll caution you away from the Lindberg 'Blue Devil' destroyer. About all it has going for it is that it is big(1:125 scale). Most of the shapes are in chunky, accurate and need to be totally rebuilt or replaced. This kit is best for R/C where accuracy doesn't matter and strenght matters more.
There are some 1:700 scale WWII Fletcher destroyers, but you mentioned 1:350 scale. I'll let you digest these things first.