Members of Unite in the so-called mixed fleet - those who have joined the airline since 2010 - walked out from midnight at Heathrow amid union claims that they are on "poverty pay".
The union accused BA of threatening sanctions against those taking industrial action.
Unite is already pursuing legal action on behalf of around 1,400 workers it says were sanctioned for going on strike earlier this year.
Unite said its action has forced BA to cancel flights and lease aircraft from Qatar Airways.
National officer Oliver Richardson said: "Vindictive threats from British Airways amount to corporate bullying from an airline more interested in punishing workers on poverty pay than addressing why cabin crew have been striking.
"Unite believes it is tantamount to a blacklisting operation and that it is unlawful. We will fight both industrially and legally to defend our members' fundamental human right to stand up to bullying and for decent pay.
"That British Airways is seeking to lease aircraft from an airline found to have breached international standards on labour and human rights, is doubly shameful.
"For an airline, which was once proud to call itself the 'world's favourite', to behave in such a way and treat its staff with such contempt shows how far British Airways has fallen from grace.
"We call on British Airways to drop the threats and drop the sanctions and resolve this long-running dispute."
BA said all its customers will be able to fly to their destinations despite the industrial action.
A statement said: "We will operate 99.5% of our schedule. Our oneworld partner Qatar Airways will be operating a small number of short-haul flights on our behalf.
"We have merged a very small number of Heathrow long-haul services and all customers affected have been notified over the past week.
"New cabin crew in their first year working full-time at British Airways receive more than £21,000 based on pay, allowances, incentive and bonus.
"This is in line with cabin crew at competitor airlines. We had reached a deal with Unite on pay, which the union said was acceptable. They should call off this unnecessary strike and allow their members to vote on the pay increase."