TLDR: they can start striking as soon as 30 days, pending the cooling off period and regulator support. They are looking for an immediate 35% pay raise with annual raises of 6%
Seriously, what in the fuck is wrong with the USA? The government has to approve a strike? What interest would the government have in approving a strike?
It's from a 1926 law targeted at Railways, and then expanded to Airlines a decade or so later. This system was originally negotiated between Unions and the railway companies with the intent to reduce disruption to critical transportation systems but it really ended up hurting the unions leverage.