Splicing them into a clip can get tricky. I find it easier to just put them on an overlay track.
The method is the same in Vegas as it is in Premiere, except with Vegas you don't have to swap out to a picture editor to create the white still. Just click on the Media Generator tab at the bottom of the screen, select Solid Color, and drag the white one onto the timeline. Then fix the location and duration.
The more subtle method would be to adjust the brightness or whiteness in the original clip. Drop the Brightness and Contrast (or maybe the HSL Adjust) video effect on to the original clip. Then work with the keyframes to cause the brightness to increase for a frame or two at the right point in time. This takes some playing around with to get it to look right, and sometimes it won't work no matter what, but the results can be better than simply flashing full-screen white.
Zalas has a good point, BTW. This is something to think twice about. Some people like to see the flashes; other people hate them. And sometimes a black "flash" is better (see the black and white section in Kusoyaro's
"Self Titled").