The howling flap here over Peter Jay's appointment as ambassador to Washington raises a familiar question: Should you take your son-in-law into the business?

On Seventh Avenue, in Whitehall, along Massachusetts Avenue, the answer is the same. It depends on the son-in-law.

In Jay's case, it must be said that the boy (just 40) has a lot of qualities. He is nice looking, like his wife Margaret, the prime minister's daughter. He always got good marks in good schools: Winchester and Christ Church, Oxford. As a salesman, he has performed well on television, notably as a commentator of "Weekend World," a Sunday news show. But how will he do on the road?

The conventional wiseacres believe that an ambassador makes no difference in an age of instant communication. If President Carter and Prime Minister Callaghan want to get in touch, it is said, they pick up a phone. The technical problems - economic, commercial, political, diplomatic - are handled by experts at each of the two missions. They deal directly with the appropriate civil servants in agencies and departments.

The wiseacres are not entirely wrong. Washington has not maintained a fully effective, full-time ambassador here for years. Over most of the last three years, the mission has been run - and capably - by Ronald Spiers, one of the State Department's most respected professionals.

But anybody who has been vocationally compelled either to serve under or to watch ambassadors at work and play knows that is not the whole story. An envoy can make a marginal difference, and economists like Jay are aware that matters are decided at the margin.

An ambassador is, above all, a reporter. He must have the wit and skill to report back with precision the posture and setting of the government to which he is accredited. He must be equally accurate in conveying to his hosts the attitudes and scene in his home county. These reports will rarely determine, but they can influence, policy in both capitals.

When the colonels seized power in Greece 10 years ago, a young and foolish king was uncertain whether to legitimize the coup. His personal advisers had been jailed. Among the few he could turn to was Phillips Talbot, the American ambassador. That night, the king permitted the colonels to swear in their puppet premier in his presence in the palace. The next day, Talbot was trying to justify the coup by telling American reporters that the highly successful Greek economy was in a parlous state.

No doubt Talbot did not act without consulting Washington. But contributing to the pro-coup policy was his evident preference for colonels to George Papandreous, the last elected premier.

Just as important as informed reporting is access to those in power at the ambassador's home capital. Kingman Brewster, for example, will be welcomed as ambassador here largely because he is of that same Yale Mafia as Secretary of State Cyrus Vance.

On the surface, no one could match Jay's access, a close family tie to the man who lifted David Owen from relative obscurity and made him foreign minister. Things, however, are not always as they seem.

Like Jay, John Kenneth Galbraith is a charming, intelligent economist-journalist. Galbraith enchanted President Kennedy with the witty letters he wrote as ambassador to India. But Kennedy did not let charm sway him entirely.

During and after the drubbing China administered to India for her border intrusions in 1962, Galbraith frequently urged that Washington enter a long-term pact undertaking to defend Delhi's air space. "It provides a long-run foundation for a political association of the first importance," the ambassador wrote privately. The President, however, was unimpressed by what could have been a bottomless pit.

On the other side, political clout and judgment can matter more than friendship or even relationship. Last winter, Spiers in London was troubled by the rigid terms that the U.S. and Treasury Secretary William Simon were demanding for the British loan from the International Monetary Fund. So Spiers prevailed on a bright if unprofessional ambassador, Anne Armstrong, to call on some countervailing force. She twice phoned Secretary of State Henry Kissinger and he paid attention to a former National Republican Committee co-chairman of proven judgment. The loan terms were duly relaxed.

Jay has made his living for the past 10 years as a journalist, and this would seem to qualify him as a diplomatic reporter of the first rank. The trouble, however, is that Jay is a commentator, rather than a reporter, and he likes to ride hobby horses hard.

He once said he would emigrate to the U.S. if Britain joined the Common Market, a judgment about the protectionist, cartel-minded community that an economist would understand better than a politician. Jay thought that John Connally came close to being the greatest Treasury Secretary since Albert Gallatin, a view that European finance ministers found eccentric. Jay has predicted the imminent fall of British democracy because of uncontrollable wage appetites by unions. This Spenglerian view was followed by two years of extraordinary union-imposed wage restraint.

Galbraith once told de Gaulle that it was very difficult for large men like themselves to avoid looking down on those of more conventional size. Jay is one of that breed. The serious question then appears to be not whether the son-in-law should come into the business but rather, will Jay allow humble facts to intrude on his loftier visions?