Question

Is there any way to increase the odds of a wild Pokemon holding an item?

Answer 1

A pokemon with the ability "compound eyes" increases the odds.

http://www.smogon.com/dp/abilities/compoundeyes

Comments

Like DarkTyphlosion said. Butterfree, Galvantula, Joltik, Yamna, Nincada, and Venonat may have this ability. Dustox will have it as a Dream World ability.

Answer 2

From Pokemon Emerald to Generation VIII, a Pokemon with Compound Eyes at the front of the party will increase these odds. In Generation VIII only, a Pokemon with Super Luck has the same function. This is the case even if a Pokemon with either Ability is fainted.

Compound Eyes (Bulbapedia)
Super Luck (Bulbapedia)