I like taking pictures of flowing water on my iPhone, and I'd like to get the soft-cloudy-blur effect for the water. On a traditional lens camera, this can be done with a longer exposure time. Is this possible on an iPhone 6s? And can you describe the process?

Something like this:

Third-party camera application

It does not appear that the default application on iOS has any fine-grained control mode. But you can achieve that if you use a third-party camera application that gives you access to it.

This page examines how to achieve the kind of control DSLR camera users are accustomed to, and it specifically mentions long exposure of water. The page recommends a few applications. But I think there are many more, so I advice you to look through reviews of third-party camera applications closely and find one that is well suited to you.

ND filter and tripod

You may also want to look at an ND filter and a phone tripod. Phone cameras are ridiculously sensitive and in daylight you will overexpose any picture with a shutter time of 1 second or more. To prevent that from happening you need an ND filter. There are plenty of ND filters that clip onto your phone.

And of course you cannot hand-hold your phone for long exposure pictures, so get a little tripod for it too.

Examples from another brand

The default camera app on my phone has a "Pro" mode that allows fine-grained control. Below is an example of where I can manually set white-balance, ISO, shutter time and a few things more.

Here are some examples of where I used that mode to deliberately extend the shutter time...

Manually set to 4 seconds, ISO 50

Manually set to 1/7 seconds, ISO 200

Manually set to 4 seconds, ISO 80

Edit, trying myself with ND filter

So I went out today to find myself a little stream to try out my new ND filter that I got after first writing this answer.

The filter was a ZOMEi 37mm variable ND filter with a clip-on adapter.

Lighting conditions were: overhead clouds about an hour before sunset.

First picture is a reference, taken on full auto with HDR.

1/50 sec, ISO-125, automatic HDR

I had to fiddle around a bit before I found a setting that worked good. But eventually, I got something reasonable, balancing the adjustable ND filter with shutter time.

4 sec, ISO-50, automatic white-balance (Click for 1920 x 1080)

I tried letting Google Photos make some of them black & white, and I am fairly happy with that...

4 sec, ISO-50, automatic white-balance, post-processed to B&W (Click for 1920 x 1080)

...but it was also with that that I realised the 10-second pictures had turned out really grainy, even with ISO-50.

10 seconds, ISO-50 (Click for 1920 x 1080)

So in conclusion: yes, using an ND filter works well to allow a phone camera to extend the shutter time. And with suitable filter and/or post-processing, you can achieve those kinds of pictures you are looking for.

But beware that the phone sensor really struggles when it has to work over a very long shutter time, and even the lowest ISO setting seems to be unable to save it from some bad graininess.

The easiest way is to take a Live Photo, then while viewing it in the Photos app, swipe up to access effects and choose Long Exposure. This will blend the frames of Live Photo together into a single image.

I'm not sure how necessary a tripod is for this; since you're expected to hold your phone while shooting, I'd imagine the stabilization+blending software is pretty good.

That particular image almost has to be a fusion of two (or more images). In order to get the blur in the water, you need a relatively long exposure time, as you mentioned. But if you've ever hung around koi ponds much, you probably know that the fish aren't going to hold still that long, and since the fish in that image are not blurred at all (other than refractive blur from being under the water), the shutter speed for that portion of the image must have been fairly fast.

Whether or not you can achieve the long exposure time on an iPhone anything, I can't really answer, as I've never used any camera app on any iPhone. But I would guess that either the built in camera app or a third party one should give you that capability somehow. I know even the built-in Android camera app allows you to do things in manual mode - I would be surprised if iPhone were less capable in that way.

The native iPhone camera app does not allow manual exposure control. You would need to use a third-party camera app to control the shutter speed. However, there is a Long Exposure effect that can be applied to Live Photos. BallpointBen describes how to use the feature.

You may also simulate long exposures by blending multiple frames together. Use the iPhone burst mode to capture a series of images by holding down the shutter button. Align and combine the images using median blending mode with tools such as Photoshop, align_image_stack, or ImageMagick. See How to Improve Your Long Exposure Photography with Photo Stacking.