According to the Monster Manual a variant Vampire spell caster can cast the Mirror Image spell. If vampires aren't reflected in mirrors and other reflective surfaces how would the vampire know how his or her mirror image should look?
Mirror image doesn't have anything to do with mirrors.
A vampire can cast mirror image just fine, despite not reflecting in mirrors. Nothing in the spell description of mirror image says that you need to be able to see your reflection to cast the spell. There is no requirement to know what you look like to cast the spell.
The description of Mirror Image doesn't say you have to know what you look like. The text says "Three illusory duplicates of yourself appear," with no qualifications.
This means that a blind creature could cast the spell just as easily.* Or, if you have a smear of chocolate on your cheek that nobody told you about, the illusory duplicates would have identical smears of chocolates on their cheeks, even though you didn't know they should be there. A vampire with no reflection can benefit from the effects of the spell in the same way, because the spell just magically knows how the duplicates should look.
*The spell description says "A creature is unaffected by this spell if it can't see," but this refers to creatures that are trying to attack the caster of the spell.