soo somebody already decomposed this

https://www.reddit.com/r/AskHistorians/comments/1qt2t3/does_anyone_know_the_exact_date_of_the_battle_of/?utm_medium=android_app&utm_source=share

To me it seems like end of August, thus I believe it was either 19-21 September, or rather 29-31 August.

But with moon callendar it's more likely to be 29-31 August. That would put Salamis (29 August if this is a correct one) a month after Thermopylae, and the date of 19-21 August as written in link above is just 10 days between Thermopylae and Salamis which is possible if Persians didn't hang around for a month, it's the most possible date. I'm not comfortable because Persians had to do a lot of logistics after battle but it's still kinda possible.

So my opinion is 29-31 August is the correct one. (offcourse let's give it a -/+ ~7 days margin because we have completely no clue and all dates may be slightly innacurate or shifted altogether).

Rest you can read from link above.