I tried to do it with OpenTK - it wanted me to have a context though, but OpenTK.Graphics.GraphicsContext.CurrentContext was always null, creating a context proved futile (probably because the SFML window already has a context) and creating a dummy context (via GraphicsContext.CreateDummyContext()) was pretty useless as one can't call MakeCurrent() on that one.
I figured that might be similar with other OpenGL wrappers, so I tried the P/Invoke. Works fine, thanks!
Just for reference for people searching for this, you simply need this piece of code:
[DllImport("opengl32.dll")]
private static extern void glFlush();
...and now you can call glFlush() in that class.
Thanks for your help, Laurent!