what is the biggest size 14 inch tires i can put on my 69 cutlass with no clearance problems?

 

Unfortunately there are not a whole lot of choices these days in 14" tires. You'll be better served with some 15" rims and going from there, and even with that the sizes are dwindling.

The stock equivalent on a 14" would be 225/70/14 and trust me they are not all that big. You can get away with a 255/60/15 on the back and run a 235/60/15 on the front and that combo looks good. I have those in a BFGoodrich Radial T/A on my 70 and it works very well.