"increasing flow of" is correct and usable in written English.
You can use it to describe a situation where there is an increase in the rate, speed, or volume of something. For example, "The increasing flow of traffic on the highway made the commute longer."
(Ironically, the most common category used in what seemed to be an ever increasing flow of misinformation was "Brain optimisation").
There were surely big fees to be made advising on how to invest the increasing flow of petrodollars.
The Indians have also put up with an increasing flow of migrants from Nepal.
A precipitous fall in the dollar is possible because the worsening current account deficit requires an increasing flow of money from abroad to cover the widening gap.
Australia's debate over how to cope with the increasing flow of asylum seekers has intensified since two boats carrying Australia-bound migrants capsized in the last two weeks.
But, stresses Pyke, the increasing flow of international money doesn't in any way diminish the role of the traditional British broadcasters.
Quito is still a relatively shy star, but new boutique hotels in old colonial mansions are already competing for the increasing flow of visitors.
President Bush's description of North Korea as part of an "axis of evil" may have created a sense of urgency about overcoming isolation, as has China's irritation over an increasing flow of North Koreans across their mutual border.
On Friday, Nepal was reported to have exempted only tarpaulins and tents from import taxes, prompting UN resident representative Jamie McGoldrick to warn the government to loosen customs restrictions to deal with the increasing flow of relief material.
But Eric Brant is already working as a misplaced miner of sorts, absorbing a vivid sunburn in politely herding the increasing flow of tourists who approach the rescue pasture as if it were Lourdes.
