It is my sad duty to inform you that there is no evidence for Roman water slides. The city of Rome had the premodern world's most impressive water supply system, with eleven aqueducts carrying hundreds of millions of gallons every day. Most of this went to public fountains. Some was diverted into the homes of the rich. Torrents streamed into the great imperial baths. But nary a drop - alas! - was turned to the purpose of causing inclined planes to become wetter and/or wilder.

Let us imagine that some Roman with a unquenchable thirst for aquatic fun has decided to sneak into an aqueduct. This is risky business - a scandal arose when Nero reportedly wallowed in the headwaters of the Marcian Aqueduct, fouling Rome's drinking water (Tac., Ann. 14.22) - but our aspiring aquanaut is determined to get his fix. First, since the water channels were normally either underground or covered with heavy stone slabs, he has to find a maintenance door. After prying this open, he descends into the humid darkness, landing in a swift and shallow stream of water. He whips off his tunic, does a flying belly-flop - and breaks his nose on the concrete floor, having signally failed to slip and slide.

The basic problem was gradient. Rome - like most Roman cities - was built on a plain, and took its water from the nearest convenient perennial springs. These were located up to 60 miles away from the city, but only a few hundred feet above it. The aqueducts thus had to slope very gently - sometimes as little as a foot each mile. Sliding under such conditions left much to be desired.

Sometimes, aqueducts were more substantially sloped. Although the Romans are famous for their great aqueduct bridges (like the Pont du Gard in southern France), they constructed inverted siphons to cross valleys too deep or broad to span with arches. These siphons funneled water under high pressure through one or more large pipes. A Roman enthusiast could conceivably have wriggled his way into one of these. But if he did, he would certainly be crushed or drowned long before his battered corpse was shot out the other end.

Romans who wanted the water slide experience were advised to travel to Egypt, where they could shoot the funnel-like rapids of the First Cataract in light boats. Closer to home, they could go to the beach at Baiae, or simply lounge in one of Rome's great imperial bath complexes. (The wastewater of the largest baths, which flowed to the sewers in foaming torrents, was sometimes used to power grain mills; but never, as far as I could discover, anything more entertaining). If all else failed, they could swim in the noxious Tiber or pilot a boat through the sewers.

For what it's worth, I talk more about aqueducts in the first few minutes of my old Baths of Caracalla video.

Without wanting to burst the bubble of any visitors from r/civ, this recent answer from u/iphikrates puts paid to the idea of ancient water slides.

I'm fairly certain the log flume predates the water slide. They were built by the logging industry during the 1800s to move logs over land to rivers and lakes. Somebody had the bright idea of putting a canoe in one and thus the first "Water Slide" was invented. However, it would have been highly dangerous. Still, mill rides based on the logging industry began to spring up in the turn of the century for amusement.

Mill rides were a lesuirely affiar, much like a tunnel of love. However, as roller coasters evolved to offer greater and greater thrills, mill rides evolved to do the same. Starting in the 1920s they evolved into Mill Chutes where at the end of the ride, a drop sends the log (canoe) down a chute in order to splash the riders.

This evolved further into the modern day log flume ride in the 60s at places such as Knotts Berry Farm in California and Six Flags in Texas.

Somewhere in this evolution, somebody had the bright idea to remove the log (canoe) and let swimmers simply ride the chutes themselves. Thus the water slide was born. Probably also coinciding with the first water parks in the 60s.

Can I just say that the reading the responses to this question has been one of the most fun and interesting experiences I’ve had on Reddit. To follow the thread from the aqueducts of Ancient Rome to the tools and calculations used by Roman surveyors to Tenochtitlan to the Hohokam to the origins of the log flume water park ride in the 19th century logging industry has truly been an exhilarating and fascinating ride. Thank you to everyone who responded