Well from a MOA standpoint, it just binds to the ribosomes in the bacteria and inhibits the transcription of RNA so I wouldn't see how kava would affect that.
It is hepatically metabolized though CYP-3A4 (I think) which kava inhibits, so it could lead to higher than intended plasma levels. That being said, taking Azithromycin for longer periods of time also results in a longer half life anyways(68hrs vs 11hr).
However, azithromycin has been shown to have potentially dangerous cardiac effects. There are a large number of drugs listed as having potentially MAJOR interactions which includes. Since we don't know exactly what effect kava has from a cardiological standpoint, I would recommend against taking them together. If kava, through some mechanism, prolongs the QT interval, the could be a potentially deadly effect.
I'm not familiar with what the cause for the cardiac effect is, but
In 2013, the FDA issued a warning saying that azithromycin "can cause abnormal changes in the electrical activity of the heart that may lead to a potentially fatal irregular heart rhythm."
Here is what worries me:
"Large doses of kava pyrones can lead to abnormal atrioventricular function, consistent with kava’s well known muscle relaxing properties. Actions of kava pyrones on voltage gated ion channels, with antagonistic effects on Na+ and Ca2+ currents and modulation of K+ currents, are of importance for their mood stabilisation properties and these cellular actions show a large overlap with the actions of established mood stabilising drugs. Antipsychotic drugs prolong QTc interval and bind to the potassium rectifier channel, and their use may be associated with torsades de pointes and sudden cardiac death."
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http://jech.bmj.com/content/58/2/140.full.pdf]
There are some anti-psychotic drugs listed under the MAJOR interactions category because of their effect on QT interval so therefore, I would recommend against it.
I feel like I'm always the debbie-downer when it comes to this stuff but I would much rather recommend caution than have people start having adverse effects or death. Not only because I care about all of my brethren here, but also (but less importantly), it would harm kava's safety record.
Feel better man!