I could find no studies supporting that claim, however I suspect it's not going to be as effective as proper medication.
Dandruff is the most commercially exploited skin disease. All the medicated shampoos use various active ingredients, either alone or in combinations. None of them list vinagre (acetic acid) as an active ingredient.
- Salicylic acid
- Salicylic acid and sulfur
- Zinc pyrithione
- Selenium sulfide
Note that all of these medications are symptomatic because dandruff is not a well-understood disease - but this doesn't mean that the mechanism of action of the active components is not well understood.
In such a commercially exploited pharmacological I sincerely doubt that a cheap, safe and miraculous cure as vinagre is purported to be is not internally studied and exploited if effective.
In fact, salicylic acid is used for its acidic properties -- similar to acetic acid. The difference here is that salicylic acid is more effective than acetic acid. In short, therefore, vinagre is quite likely to be a less effective symptomatic cure, with respect to the pharmacological alternatives. From the linked paper:
Salicylic acid is a [...] acid keratinolytic agent that is useful in removing scaly hyperkeratotic skin. It decreases cell-to-cell adhesion between corneocytes.