If we reject the notion that gender roles exist, how is gender fluid a thing?

It's a thing because gender identity and gender expression are not the same thing (and gender roles are completely separate from both of them).

Gender identity is who you are.
Gender expression is how you look.
Gender roles are what you do.

If you feel like a woman, that's your gender identity.
If you dress like a woman, that's your gender expression.
If you spend most of your day in the kitchen because you think society expects that of you, that's your gender role.

For most people, gender identity and gender expression match up, and to a lesser extent, gender roles often match up with both identity and expression (though that's changed quite a bit over the years). That is not, however, always the case. And the fact that they differ far less often than they match doesn't make the cases where they do differ any less valid.

It is entirely possible for someone to fluctuate in their gender identity from day to day... that's what "genderfluid" means. Sometimes you might feel more masculine, sometimes more feminine, and this can come just as much from internal biology (hormones and the like) as from external whims (just being in that mood where you feel like dressing up a certain way). There aren't many people that are like this compared to those who aren't, but that doesn't mean they don't exist.

The problem is that we don't really have a very organized set of labels for all this, because we're still in the middle of figuring it all out. Genderfluid, for example, can refer to both someone whose gender identity is fluid and to someone whose gender expression is fluid, because the same word (gender) is used in so many different ways.

What makes you a male or a female (or anything in between)? Is it the way you dress/style your hair/job/hobbies?

No. Continuing the explanation, male and female - at least these days - is mostly used to refer to sex, while man and woman are used to refer to gender. The difference being that sex is your physical shape. So you can, for example, be a male woman (with a male body but a feminine gender identity). Again, this is a relatively new way of defining things, because it's only relatively recently that we've really been able to explore these sorts of things without getting stoned to death in the street (sometimes literally).

On a side note: gender roles exist, but they are entirely arbitrary. We invented them, they're not some aspect of our very nature. "Men should work, women should tend house." is not a natural state of being, it's just how we ended up dividing things based on loose perceptions of who should be doing what, based on associations like "Women give birth, so they should rear children." and "Men are usually bigger, so they should do the physical labor." The fact that gender roles are unnecessary (at least these days) and arbitrary and almost entirely socially designed doesn't mean they don't exist, it just means that we don't need them around anymore.