In the three months since the start of the strike against the Norfolk & Western Railway, Fred Kroll, the president of the Brotherhood of Railway and Airline Clerks, has done little to endear himself to his fellow union presidents.

"He's taking dancing lessons at the expense of all the other unions," one union leader said yesterday as the rail dispute appeared headed toward Congress for settlement. "He's got everybody mad at him with the unorthodox, mismanaged way he's handled the strike."

The views of other union officials tended to be less kind.

Within the Carter administration, however, there appeared to be a general respect for Kroll and his knowledge of the industry. Mediators involved in the government's last-ditch effort to voluntarily settle the dispute this week said they were impressed by Kroll's performance.

For Kroll, the escalating strike appears to be a matter of potential survival. "I think they're trying to test my mettle," he tells colleagues," and I'll show them."

One of the youngest presidents of a major union, the 42-year-old Kroll has yet to stand for election before his entire union membership - a fact many in the labor movement believe has dictated his behavior in the current strike.

Kroll was elected president of BRAC by delegates to its 1976 convention to fill the unexpired term of C.L. Dennis, who was ousted in a bitter, behind-the-scenes political struggle. Dennis, many BRAC officials say, was forced out after he tried to assure that his son would become president of the union at the next election in 1979.

Ever since his election, Kroll has been trying to solidify his political base within the union.

Like many of the union presidents who have risen to power in recent years, Kroll is something of a technocrat - well versed in the problems of his own industry, but with little influence in the trade union movement.

A former IBM operator with the Pennsylvania Railroad, Kroll rose through the union ranks without ever leaving his native Philadelphia. He still maintains his home there, commuting from Washington every weekend.

And at the AFL-CIO headquarters, where the clerks union maintains its Washington offices, Kroll is still viewed, in the words of one federation official, as "the brand new kid on the block."