Pretty straight forward question. By RAW, is it possible to increase the AC of the duplicates created by mirror image or they will always have an AC equal to 10 + Dex modifier? Be it using other spells, magic items or other effects.
The only way to do so is to increase your DEX modifier.
The spell clearly states:
A duplicate's AC equals 10 + your Dexterity modifier.
This is very explicit. D&D operates under the rule of "Specific Beats General" (PHB p. 7), meaning that in this case, you could change the formula if you found a feature that explicitly changed the AC of a Mirror Image illusion, or generally changed the AC of any illusion created by the caster.
However, to my knowledge, there is no feature or ability in any of the official rulebooks that I can think of that would have such an effect. The most likely place to find such a feature would be an illusion wizard's class features, but they disappoint in this regard.
Hence, the AC will always be calculated as \$\left(10 + DEX\right)\$, and since 10 is obviously constant, the only possibility left is to increase your DEX modifier. You can do that for example with ASIs you get from leveling up, equipping items that raise your DEX stat, or using magic items that permanently raise your DEX.
Examples for such items would be an Ioun Stone (raises DEX by 2, up to 20, while worn) or the Manual of Quickness of Action (permanently raises DEX & maximum DEX score by 2).
You can also hide your duplicates behind cover to increase their AC.
Half cover increases their AC by 2, while 3/4 cover increases it by 5. They are valid for the Cover rules (PHB p. 196), since those reference targets in general - not just creatures.
See Mark Wells' answer for details.
Hide behind something.
Partial cover provides a direct bonus of +2 to +5 AC. The illusions follow wherever you go, so they'll follow you behind cover.
Other than that, not really.
They're not solid, so they can't wear armor. (If the caster wears armor, they will have illusory armor, but it doesn't help them.)
They're not real creatures, so they don't benefit from spells like mage armor and barkskin that are designed to work on creatures.
They aren't monks or barbarians so they don't get Unarmored Defense.
Making them invisible / turning off the lights will make them entirely impossible to hit, since they're just visual illusions, but that's not a change in AC.