Doug,
A 345 profile tire has a section width of 13.9" and is for a recommended rim width of 11.5" to 13.5".
I'm running 335/35-17's on a non flared car, so I suspect the tire width is not the issue, just you'll need some wider rims with the correct backspacing to mount them on! Then if you had to get rims, why would you go 15"?
Julian
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