I picked them because they are all similar to critters in the area: ciceda come to Kentucky every four years or so. Ekans was the closest I could find to the cottonhead. The patrat is based on all the groundhogs we have. They're mostly in parks and other cities but they're abundant because people have stopped killing them and they reproduce quickly.
I hope they're in Kentucky but I'm willing to change any pokemon that need to be, obviously
So, I just did the check, and unfortunately, all three of you Pokemon aren't located nearby. Especially the Ekans and Nincada. I placed those two Pokemon more based on there evolved forms (Arbok being a Cobra, and the Nincada line taking inspiration from Ninjas). Both of these Pokemon are found in Asia, and Ekans are also found in Africa.
Patrat on the other hand is found just a couple states West of Kentucky in the Great Plains area of the USA. So it is entirely possible that some ventured to Kentucky or that your character visited that area and caught one while he was there.
Here is a list of Pokemon that are within Kentucky and surrounding states. This is a little wider radius than I normally do, but it gives you a great selection I hope...
Bulbasaur (Uncommon) Forests
Caterpie (Common) Forests / Grass
Weedle (Common) Forests / Grass
Pidgey (Uncommon) Anywhere
Rattatta (Common) Anywhere
Psyduck (Uncommon) Rivers
Magnemite (Rare) Cities
Ghastly (Rare) Night / Graveyards
Spinarak (Common) Forests
Snubull (Common) Parks / Grass / Forests
Heracross (Uncommon) Forests
Smeargle (Uncommon) Anywhere
Zigzagoon (Uncommon) Forests / Grass / Suburbs
Sableye (Common) Night / Caves
Mawile (Common) Night / Caves
Shuppet (Uncommon) Night / Suburbs
Bidoof (Uncommon) Rivers
Shinx (Uncommon) Mountains / Forests
Buneary (Uncommon) Where the Bunnies are.
Carnivine (Common) Forests
Rotom (Uncommon) Cities / Suburbs
Snivy (Rare) Forests / Grass
Drilbur (Uncommon) Mountains / Grass / Forests
Timburr (Rare) Forests
Scraggy (Common) Night / Cities
Deerling (Common) Forests / Grass
Litwick (Rare) Night / Cities / Suburbs
Rufflet (Uncommon) Forests / Mountains
Swirlix (Common) Cities / Suburbs
Clauncher (Rare) Rivers
Helioptile (Uncommon) Grass / Mountains
Togedemaru (Common) Cities