The phrase "gain backing from" is correct and usable in written English.
It is used in the context of obtaining support or approval from someone or some organization. For example, "The candidate needed to gain backing from the local residents in order to win the election."
Top performers such as Katy Perry and Beyoncé came out in support of Clinton, with Trump struggling to gain backing from mainstream acts.
Over the past month, even as he sought to avoid arrest by going into hiding, he continued the Brotherhood's efforts to gain backing from overseas by posting links on Twitter to photographs and video clips that called for the restoration of Mr. Morsi, an Islamist.
The intent is to gain backing from the Trump administration.
But the practice is increasingly gaining backing from some of the country's top law firms, which had previously viewed the business with caution.
Peasants in one commune there secretly started parcelling out land, expecting death for it, but soon gained backing from a provincial leader and Deng ally, Wan Li.
A European parliament resolution calling for an EU-wide ban on microbeads has gained backing from 340 of the 751 MEPs.
Although still probably several years away from commercial feasibility, WiMax has gained backing from heavyweights such as Intel and Nortel; Intel expects to ship WiMax chipsets by next year.
"What would it have been like if someone had filmed Bill Clinton's first campaign?" To make the documentary, Mr. Curry took a leave of absence from his job, eventually quitting altogether after gaining backing from PBS.
The European Union gained backing from the Bush administration on Monday for its proposal that the issues of investment and competition policy be included in the new round of talks.
In recent days, General Hifter has gained backing from key Libyan army and air force units, important militias and senior members of the regional security forces, as well as oblique endorsements from some leaders of the 2011 revolution.
Sinn Fein cannot be truly committed to peace if it continues to have an armed force behind it, goes the argument that has in recent months gained backing from Catholic leaders, the Irish press and what is referred to as "Irish America".
