By Pranav Kashyap

Aug 26 (Reuters) - Most Latin American currencies clung to the flat line even as the dollar slipped on Tuesday, while stocks were mixed as investors weighed concerns about the Fed's independence alongside fresh local data.

Brazil's real BRL= slipped 0.1%, giving up early gains that had potentially put it on course for a fifth straight session of gains - its longest winning streak in nearly three months.

Fresh data showed Brazil's mid-month consumer price index fell for the first time in two years, with annual inflation dipping below 5% for the first time since February. That brings it close to the upper end of the central bank's target range of 3% plus or minus 1.5 percentage points.

The drop offers a welcome reprieve for Brazil's central bank, which has kept interest rates at 15% - the highest since July 2006 - in a bid to tame persistent price pressures.

Stocks in Brazil .BVSP, however fell 0.3%.

Separately, Brazil's current account deficit widened sharply in July.

The dollar =USD dipped 0.3% as markets tiptoed into risk-off mode, but most regional currencies were in a holding pattern after a fresh shot at the Fed's independence rattled nerves.

President Donald Trump said he was firing Fed Governor Lisa Cook, a fresh jab that stoked doubts about policy autonomy and U.S. assets. Gold XAU= jumped to a two-week high.

The MSCI gauge for Latin American currencies .MILA00000CUS slipped 0.3%, while a similar gauge for equities for .MILA00000PUS fell 0.7%.

"Trump's attempt to fire Cook looks set to go to the courts, which will determine the extent and limits of the administration's ability to influence monetary policy," said analysts at Capital Economics.

"It is clear that we are heading back to a world in which the Fed is far more politicised. That risks greater uncertainty about the interest rate outlook and, by extension, higher long-term interest rates."

The Argentine peso ARS=RASL rebounded 0.89% after shedding nearly 5% in the past four sessions, as corruption allegations shook its political landscape and financial markets.

Stocks in Buenos Aires .MERV fell nearly 1%, and were pinned at an over-one month low hit in the previous session.

In a bid to stabilize the financial system, the central bank raised the amount of interest-bearing reserves banks must hold as President Javier Milei faced renewed political heat two months ahead of key legislative elections.

The corruption allegations threatened to embroil people close to the libertarian president, whose economic policies have boosted financial markets.

With midterm elections in October and a pivotal Buenos Aires provincial vote looming, the scandal comes at a critical time for Milei's party, which wants to increase its presence in the opposition-controlled Congress.

Meanwhile, Mexican equities .MXX were steady after logging their biggest daily fall in nearly three months on Monday. The country's peso was marginally higher.

Key Latin American stock indexes and currencies:

(Reporting by Pranav Kashyap in Bengaluru;Editing by Helen Popper)

((pranav.kashyap@tr.com; +919886482111;))