What configuration would limit my DSLR's shutter speed to 1/200?

Basically all digital cameras are set in a range of 1/160 to 1/250 shutter speed when flash is placed. That is calculated due to the shutter speed versus flash light bouncing back to your sensor. It comes as factory setting and there are some tricks to bend that. Because of this attribute, in any mode, the camera takes the shutter speed-when shutter speed is given below factory setting- to the safe zone.

For Canon since you asked for it there is Highspeed mode on Canon flashes where you can get up to 1/1250 safely depending to the flash model and object distance. Also without using the hotshoe and connecting the flash from side trigger, you can get up to 1/320 safely, 1/400 and 1/500 at your own risk.

Also there are some triggers and their special softwares delaying the shutter to sync with the flash for lower shutter speeds. For that I could not make any of those work properly with canon below 1/1250 shutter speed on canon mkII, mkIII, 7D, IdmkIV but on nikon d300 and d3x, I have tested up to 1/4000 without any problems.

The camera is automatically setting the shutter speed (Tv for time value) to the flash sync speed of the camera. This is the fastest Tv for which the shutter's first curtain is all the way open before the second curtain begins to close. For Tvs higher than that, the second curtain begins closing before the first curtain is fully open. This allows an effective Tv much faster than the curtains are physically capable of crossing the image plane. The faster the Tv, the closer together the two curtains fire and the narrower the slit between them is that allows light to strike the sensor as they cross it. Even though it takes much longer than 1/4000 sec for the slit to cross the sensor, any single spot on the sensor is only exposed to light for 1/4000 second.

Since the flash duration is for much less time than the time it actually takes the shutter curtains to cross the sensor, if the flash fires once while a Tv higher than the sync speed is being used only the portion of the sensor that is exposed by the gap between the two curtains as they cross the sensor will absorb light from the flash. The portions of the sensor that are covered when the flash fires will only catch the ambient light if there is any.

This question illustrates what a rolling shutter looks like. The example is based on a horizontal shutter like most film SLR cameras had. Most DSLRs have vertical travel shutters that allow for faster sync speeds, since they have less distance to travel.

What this means in practical terms:

1. If you are shooting in very low to no ambient lighting the shutter speed isn't going to affect much. It is the flash duration that will affect how much motion of the subject is captured and how bright the exposure is.
2. Almost all flash guns control power by how long the flash stays on. 1/2 power is as bright as full power, but it only stays lit for roughly 1/2 as long. 1/4 power stays lit for roughly 1/4 as long and so forth. (Yes, this is extremely oversimplified, but does get the point across that the flash is just as bright but doesn't stay on for as long when set to lower power.)
3. With little to no ambient lighting, if the flash duration is too long and subject motion is evident in your photo, try powering down the flash and opening the aperture or boosting the ISO by the same amount. Each division in flash power is one full stop. 1/2 power is one stop less than full power, 1/4 is one less stop than 1/2 (and two less stops than full), 1/8 is one less stop than 1/4 (and three less stops than full), and so on. So if you reduce your flash from full to 1/4 power then open up the aperture by two stops or increase the ISO by two stops (or combine aperture and ISO for a total of two stops).
4. If your flash is capable of high speed sync you can use it and increase your shutter speed. High speed sync uses several smaller pulses of light to illuminate each section of the sensor as the slit between the shutters cross it. If your subject is moving this could result in rolling shutter effect. Using high speed sync reduces the total available power of the flash

1/200 is your camera's flash sync speed. It is the fastest shutter speed you SHOULD use with flash.

There are special modes you can enable which will let you shoot at faster then your sync speed - Canon calls it high Speed/FP flash sync. There are problems that arise with enabling high speed modes. The biggest one is that not all of the light from the flash will contribute to the exposure, which will impact your ability to properly light up your subject.

For more information see: The Importance of Flash Sync Speed.

With Flash enabled, the shutter speed is limited to 1/200. In order to utilise the full range of shutter speeds the camera is capable of, "Flash function" has to be disabled in the menu. Keep in mind that the flash will now not work until you enable it again.