Syria had their own chemical weapons program, in addition to whatever they got from Saddam. That being said, there were massive convoys between Iraq and Syria for months before the 2nd Gulf war, while France delayed us from action. There were undoubtedly large amounts of chemical weapons that were moved form Iraq to Syria, during that time.
The frustrating thing is that MSM meme was there were no WMD in Iraq and the Bush administration was totally passive in accepting that meme despite all evidence to the contrary. Not only did they never make the case for the transfer in the months leading up to the war, but they also just accepted the media judgement that the weapons they did find never met the ‘threshold’. There were several finds of caches of chemical weapons but they were always characterized as too small or too old to matter. There were numerous finds of missile technology that Iraq was prohibited from having after the 1st Gulf war, but the media reaction was always ‘well that just missile technology, its not WMD’. There were even some biological weapons labs that were found, but the reaction was ‘well maybe they were working on civilian medical projects’.
GWB made many mistakes, but maybe his greatest mistake that we are still living with is he spent his second term totally passive in terms of letting the media paint him and his policies (and by extensive all conservatives) as inept and wrong. To a large extent, that four year silence on the part of GWB gave us the disastrous electoral outcome of 2008.