The current top answer from BigMadAndy has some solid points but approaches this entirely from the negative direction, which I don't feel is as helpful.
How should I answer a question like this?
By pivoting your perspective.
Under your concept of conflict, you've never had "a conflict". That's fine. But to succeed at interview situations, you need to consider both what an interviewer/interview process is seeking to uncover, and how you can use that to show something of yourself to your own best advantage.
It's easy to get stuck in a mode where every interview question is a possible trap or pitfall. But remember, ideally an employer is looking to learn more about you, who is a nearly complete unknown to them. This is your one chance to make a first impression by talking about yourself, and every question is an opportunity where simply replying "I don't" has wasted that opportunity (even before we get into the more negative possible interpretations of saying "I don't" to a question like this one).
So take a second and consider: "how does this question allow me to show myself in a positive light"? and you will have the core answer to your question here.
What could your handling of "a conflict" reveal that's positive to you?
So, you've never had what you consider to be a "conflict" at work. But does answering that way really help you (ignoring, for the moment, whether it potentially hurts you in the eyes of the interviewer)?
If you expand your definition of conflict to "lesser" conflicts than what you define one as, are their opportunities to underscore your interpersonal skills?
I would say that there are. Managing disagreement and arguing positions productively are incredibly important skills, and this question your opportunity to showcase your own related abilities. What situations have you been in where multiple people disagreed (maybe you were even a neutral party!), and you helped arrive at a positive solution?
Pivot and reframe the question by answering it in a way that suits you
There is still plenty of room for you to open with "Well I've never been in what I would consider a 'conflict' at work, but certainly there are times where it requires some persuasion to reach an agreement, and there's one time in particular that comes to mind: ...", if you want to underscore that you haven't had any severe arguments or rows at work.
A word of caution: when pivoting by changing the framing of your answer, you need to consider the contextual intents of the original question. This works because disagreements are, from a certain point of context, still "conflicts". You need to give the interviewer the opportunity to say you answered the question well, not "interviewee went off on unrelated tangent and failed to answer the question" (been there, had to write that). There's an art by degrees to reading between the lines of what's being asked for how far you can push re-contextualizing your answer while still effectively answering to the intent behind the original question's wording. Pay attention to the interviewer's body language, if you're not going to express your choice in reframing as a possible question (lilting the end of the premised reframe, with a pause for interjection before proceeding).