There is no burning software (nor a burner) able to transform bad quality discs into good media.
If your burner is not able to write on these discs, the only solution is to get rid of them and buy only quality discs. Verbatim and Taiyo Yuden are the very best quality media available in the market. All other brands have a quality widely variable from ugly to decent.
Updating the burner firmware can improve burning quality, so this is another thing you can try.
I never used DVDFlick, so I don’t know if it also has a burning engine. If latest version is not able to solve the problem, maybe you can consider to send more detailed information to the developers, so bugs can be corrected in next versions.
If the errors you get are only when you try to burn files, maybe a good alternative could be to save converted files on HDD and then use a proper burning software to burn files. I suggest ImgBurn (one of the best software available, and it’s also free :))
btw, what errors do you get exactly? Do you get some specific error messages from the software?