That’s a flat adverb. There’s no -ly on the end of it. There can be, sure, as “slowly,” but “slow” is used adverbially and there’s not a thing wrong with it under the right circumstances.
You’ll not find it in academic writing, or formal business writing, or legal writing. Those use a register sometimes called “frozen,” meaning there are certain expected phrasings that are never changed. Think about the language of a church ritual (the more rigid the denomination, the more likely you’ll hear that frozen register). It’s always said this way, never that way. It’s tradition. It’s frozen in time. Part of the hubbub about Vatican II was over the loss of the frozen register, changing from Latin to English (or whatever the local language was). “It’s not said the same now!” Nope, it’s not. But it means the same thing, right? (That’s really a different topic, so I’ll stop with the digression.)
As much as I love flat adverbs, I don’t push them where they’re neither wanted nor needed. If a client uses them, I do my best to leave them alone unless, as happens in some cases, they just don’t work well. If a client doesn’t use them, far be it from me to suggest them; it’s not my voice in their work. It’s their voice. Their work. My task is to provide clarity, and changing “slow” to “slowly” is unlikely to help. Ditto for changing “slowly” to “slow” unless, maybe, it’s in dialogue and I’ve got a handle on the character’s style and it makes sense to suggest the change. Not make it. Suggest it.
Here’s a well-written article about flat adverbs, over at Daily Writing Tips. I see no reason to write another one. I’m just putting it out there for folks that I’m a proponent of them in cases where they make good sense and sound natural. Note that not all adverbs can be flat, and not all flat adverbs mean the same thing as their -ly counterparts. Here’s one example from the linked article: You can dress sharp, or you can dress sharply, but you arrive at five o’clock sharp.