Using the same setting, my 600d takes about 10 secs from flash to preview picture if I shoot with a high aperture of f/22. But if I shoot with the same settings at f/3.5, I can see the picture preview immediately.
Google has failed me.
It's most likely to be because at f/22, the aperture size is much smaller, therefore the shutter speed is likely to be slowed down to allow the same amount of light to get in. At f/3.5, the aperture is wide open, therefore it doesn't take as long for the sensor to gather the same amount of light to produce an image exposed in the same way.
Take a look at the accepted answer to this question about the exposure triangle for how adjusting one setting (eg aperture) means you have to adjust another setting (either ISO or shutter speed) by an equivalent amount What is the "exposure triangle"?
You could be triggering the camera to apply Long Exposure Noise Reduction to the f/22 photo because of a lower signal-to-noise ratio. When LENR is set to Auto the camera bases the decision of whether to subtract a dark frame from the exposed frame based on several variables including not only shutter speed, but also ISO and the amount of light measured by the camera's meter. If LENR is set to "On", it will be applied to every image with a shutter time of one second or longer. LENR will double the shutter time because after the shutter closes a "dark" exposure with the same ISO and shutter time is made and subtracted from the exposure when the shutter was open. For more about LENR please see What's the best way to deal with hot/stuck pixels in long exposure night photographs?
Even if you have the built-in flash set to "automatic" (E-TTL?), the brightest a flash can illuminate a subject is at that flash's full power. If the camera computes that more power is needed than the maximum the flash can provide, there's not much it can do to add more light. If the camera computes the image will be dark even at full power it may apply LENR at certain shutter speeds.