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There are likely at least two issues at play here.

First, look at the other elements in the photo. The candelabra, the window behind it, the edge of the windowsill. *All of those* are fairly sharp, with much more well-defined edges than the candle flames. Blur to the flames due to camera motion therefore seems unlikely.

Second, you probably know this, but remember that the "flame" is actually mostly *still burning soot*. Air convection carries the flame upward, but there might still be some turbulence around it which could cause some of that to drift off to the sides. When you're looking at the flame, your eyes adjust to the brightness of the flame, but the camera records what's actually there without, beyond the autoexposure system, caring (much) about the brightness in any particular spot.

So "the subject is obviously not moving" isn't really true if by "the subject" we mean the flames that you're trying to capture.

**To reduce motion blur, you need to use a shorter exposure time. However,** because less light is captured during a shorter exposure, this also makes the picture darker overall, which you'll need to compensate either by increasing light sensitivity ("ISO"), by using a larger aperture (lower f/-number), or adding more light from elsewhere, or more than one of those. Which exact choice you make depends on the effect you're after.

As an experiment, I would suggest using whatever settings you have access to to reduce the exposure time used when taking the picture. If you don't do anything else, the picture will probably come out dark, but that's okay for the moment. A 1/500 or 1/1000 second exposure might be a good starting point. Look at the flames; they should be more distinct.

Assuming that works, then consider how you can brighten the capture back up. I would suggest increasing the aperture size (decreasing the f/-number; f/2 is a larger size aperture than f/4) if possible, and second to that, increasing the sensitivity setting (the "ISO" number). Increasing the aperture size will reduce the depth of field, but it looks like you've got plenty enough depth of field that this won't be an issue. (With their small sensors, cellphone cameras typically have very large depth of field to begin with.) Increasing sensitivity will increase image noise, which is why it's usually a good idea to keep the sensitivity as low as possible to get the exposure you want.

If all else fails, shine a diffuse light toward the scene to increase the overall brightness, then darken the image in post-processing. Shining a flightlight onto the ceiling above the scene should work okay without introducing too much in the way of shadows, reflections or glare.