When you've got a flat on a clincher wheel, it's best to bring the bike to a stop without using the brake on the flat wheel. Using the brake will slow the wheel, but not necessarily the tire, ie the tire may start precessing around the rim. In that case, the brake isn't really slowing you down, but it may have very unpleasant effects on the tire and tube. The valve could be stripped off the tube. In extreme cases, the tire and/or tube could come off the rim and wrap around the hub or frame. We occasionally see a bike like this in the shop, usually an MTB. If you've got a flat, don't keep riding on it, but don't panic brake. Instead, brake gradually to a stop and change the tube.