Hasn't happened with mine yet. I've run at least a few kegs through each of the lines (I have three taps to feed). Using 3/16" ID Bevlex tubing on mine ('beer line').
For cleaning my lines, I run a warm (not hot since I clean the inside of the keg with it too) PBW solution (1.5-2oz per gallon strength) through them (at least 2 quarts worth). I let that rest for 5-10 minutes then rinse with cool-warm tap water. Followed by at least 2 quarts of StarSan solution, which is left in the line for at least 10 minutes. I then just hook up a new keg and push the StarSan solution out. I push everything through the lines from a keg, under at least 10-12psi.
Try soaking the lines in PBW and then StarSan solutions. You probably don't need to worry about it right now, but when the keg kicks, try the method I listed above. Even though the SuperFlush may [normally] be good stuff, you might have a bad batch, or it could be at lower strength than it should be. If the lines get cleaned up with the other solutions, then you know it's not the lines themselves that's the issue.