I disagree about the oil flowing in Iraq. If it's flowing it's being "stolen".

What Syria has been doing is being less of a target than Iran. Syria is not behaving "better" if Israeli attacks on their alleged nuclear facility are to be believed.

Lastly, China has not been blocked from Iraq at all. In some ways, the Iraqis seem to be viewing China as their "best option" partner for oil exploration and exploitation.

For example:

Oct 2006: Iraq, China to revive Saddam-era oil deal as Baghdad seeks investment

China and Iraq are reviving a 1997 deal worth US$1.2 billion (€850 million) signed by Beijing and Saddam Hussein's government to develop an Iraqi oil field, Baghdad's oil minister said Saturday.

Officials will meet next month to renegotiate the agreement over the al-Ahdab field, said Iraqi Oil Minister Hussain al-Shahristani. He was wrapping up a three-nation tour to secure investment to revive his country's oil industry...

The new Baghdad government courted Beijing because Chinese producers have been willing to invest in Angola, Sudan and other countries that are considered too dangerous or politically isolated...

Beijing had been thought to be out of the running for major contracts in postwar Iraq...

April 2008: Iraq qualifies four Chinese companies for oil contracts

Four Chinese oil companies were among 35 companies that qualified to participate in Iraq's coming licensing round for oil and gas contracts, the Iraqi Oil Ministry said on Tuesday.

A statement issued by the ministry said that CNOOC China LTD, CNPC, Sinochem and Sinopec Group won rights to bid tenders to develop oil and gas fields in Iraq.

From 120 applicants around the world, only 35 companies and consortia, were qualified in accordance to criteria put by the Iraqi Oil Ministry, according to the statement.

Plus, as you note, China has been securing oil resources everywhere else in the world too.