In his final public appearance before retiring as chairman of the Federal Reserve Board, Arthur Burns emphasized once more his strongly held views on the "special status" of the Fed - meaning its oft-disputed autonomy.

The chairman, who has become almost a Washington institution, told members of the National Press Club that the Fed must be able to act not only independently of the executive branch, but "also with immunity from translent congressional pressures."

That, he argued, was what Congress had in mind when it created the Federal Reserve System back in 1913. Be that as it may, it is no loner the prevailing sentiment on either Capitol Hill or at the White House, where there is a growing feeling that the free wheeling of the Fed must yield to synchronizing its activities more effectively with presidential and legislative goals.

There is little doubt that Burn's successor, G. William Miller, has got the message. At a confirmation hearing a few days ago, he left no doubt that the new order of the day will be "cooperating" with the otehr branches of government. It was just what the senators wanted to hear.

Miller, who is not professional economist, made it plant that he would probably adjust the Fed's monetary policies to the administration's fiscal policies more than his predecessor did. In the coming months, both the President and Congress are going to be concentrating on unemployment, even to giving it precedence over inflation, if necessary. They won't encounter any resistance from Miller, who as chairman of a large corporation. Textron, Inc., has already shown that he shares the same priorities.

In any case, no new chairman of the Fed will be in a position to run his own show as majestically as Burns, whose authority rested not so much on his statutory powers as on personal prestige and his unique standing in the banking and business worlds.

Both friends, and foes have called him "the second most powerful man" in Washington, although there is nothing in the law making him so. But he is the first head of the Fed to be economic scholar, and a renowned one at that. He has served under four Presidents, Republican and Democratic alike, and has spent the better part of two decades in Washington as chairman of the Council of Economic Advisers (Eisenhower), White House counselor (Nixon) and chairman of the Federal Reserve Board (Nixon-Ford-Carter).

All that has been enchanced by a charm of personality, a way with the press and histrionic gifts as a pipe-smoking congressinal witness. In the last few years, he has needed all of his political savvy to haead off repeated efforts to rein in the Fed.

Nobody knows better than be that what Congress and the President giveth, they can take away, the first by rewriting the Fed's charter, the second by changing its directors. There is, inevitably, a price for not playing ball with the White House, and Burns has just paid it. He was not reappointed chairman.

In 1975, believing rightly or wrongly that Burns's tight-money policy was retarding economic recovery, the House approved (279 to 65) a Federal Reserve Reform Act, which the resourceful chairman successfully defanged, but it showed which way the wind was blowing.

One important change now requires that Fed to inform Congress at quarterly intervals as the board's monetary and credit targets. Another new provision subjects the chairmanship to Senate confirmation. Moreover, passage of the Humphrey-Hawkins bill, now thought certain, will compel the Fed to report each year to Congress on how its programs will lead to full employment by 1983.

Other proposals, currently on hold, would cut the 14-year terms of the directors in half, call for labor, farm and consumer representation on the board, and require it to conduct its business in open session.

In fairness to Burns, it should be acknowledged that, on balance, he has not been as rigid as his critics sometimes contend, nor as partisan.

Although he owes all of his high government posts to Republican Presidents, the record shows that he didn't hesitate to disagree with them publicly. He spoke as bluntly to Nixon and Ford as he has to Carter.

As to flexibility, few seem to remember that he has, at different times, supported a form of government-guaranteed employment and also advocated a "national income" policy to keep wages and prices in line, albeit this side of out-right government controls.

Looking to the future, Prof. Paul Samuelson, the Nobel laureate in economics, told the House Banking Committee that "the Federal Reserve must either be made responsible to the executive itself or must be on a short string in its responsibility to the Congress." That's about the way things a re shaping up.