Answer:
Everything that grows from the ground is kosher. Concerning the pickles only,
there's nothing in a pickle that makes it non-kosher, as long as it doesn't come
in contact with other ingredients, or machinery, used in non-kosher products.
But just like anything else on the supermarket shelf, one has to check to make sure.
Kosher pickles should be kosher. To confirm this, you would need to check the labeling
for a recognized hechsher (kosher certification symbol). The US, and most other countries
with food labeling laws, doesn't allow any reference to being kosher unless the product
is certified kosher. Pickles that are labeled "kosher style", are most likely not kosher.
Items that could render pickles not kosher are primarily non-kosher spices and non-
kosher vinegar.