I would write (for example)
Having a full driving license, life insurance, 5 years of driving experience, and having never had an accident, surely I am a great driver.
Having a full license, life insurance, 5 years experience, and no accidents, surely I am a great driver.
Some differences depend on locale, such as driving or driver's and licence or license. Also, "I am a great driver" is likely to be seen as conceited or facetious.
Regarding your specific question ("Is this use of having correct in explaining that I have this, this and this"), your usage of it was mostly correct, but the last clause of the list had a problem. For more about parallelism in lists, see (eg) english.purdue on Parallel Structure, or a Parallelism webpage at kentlaw.edu.