The Canon extenders will not physically mount to an EF-S lens. Even if you defeat the keying the front part of the EF 2X (any of the three successive versions) would extend into the rear of the EF-S 55-250mm and almost surely contact and damage the rear lens element or the front element of the extender or both, at least at certain focal length and focus distance combinations.

In 2015 Kenko introduced Teleplus HD DGX 1.4X (and its 2.0X counterpart). These teleconverters officially support some EF-S and EF lenses. There is an exhaustive compatibility list on their website.

Some third party teleconverters, such as the older Kenko AF 2X Teleplus PRO 300 DGX Teleconverter for Canon, are not officially supported. They might or might not fit your EF-S lenses but then you have other issues to worry about.

• Your 55-250mm f/4-5.6 lens becomes, effectively, a 110-500mm f/8-11 lens. This means your camera would be unable to use autofocus and the viewfinder would be very dim when trying to manually focus. You might be able to use magnified Live View to manually focus.

• The EF-S 55-250mm f/4-5.6, while a pretty good lens for the price, probably isn't of a high enough optical quality to accept a 2X converter and give you results you would be happy with. All of the flaws of the lens are magnified along with the image it projects. Sharpness would suffer. You also would give up a little contrast. Chromatic aberration (purple fringing) would likely be increased.