Kim Splain and Junior Wyatt, stepping lightly in the brilliant sun of a cool spring day, their Army-surplus canteens swinging from drab green knapsacks on their backs, rounded the Lincoln Memorial on their way to the Consitution Gardens.

They had come 818 miles in six weeks from American Legion Post 279 in Jacksonville, Ill. tramping through snow and rain and wearing out a pair of jogging shoes each as they followed Route 50 in from Cincinnati.

And now they received a hero's welcome, if only a bit too late.

Splain and Wyatt are veterans, survivors of the era when the Vietnam war divided the nation. When they came home -- Splain in 1973 and Wyatt in 1968 -- "nobody much paid attention, except for my family," Wyatt said.

But yesterday, on the National Day of Recognition for Veterans of the Vietnam Era -- proclaimed hastily by Congress after the American hostages herelded return from Iran -- Splain and Wyatt took their seats with the rest of the dignitaries, bowing their heads reverently through the pomp of a Washington ceremony.

Their walk was a stunt for publicity, but they felt it was a good cause, said Splain, 28, an unemployed truck driver and Wyatt, 34, an unemployed bartender.

They hope to raise $7 million for a memorial to Vietnam veterans that would be erected on two acres of National Park Service land in the shadow of the Lincoln Memorial. On the marble icon would be inscribed the names of the 57,000 U.S. servicemen and women who were killed in the Vietnam War.

Marching off at 1 p.m. from Arlington National Cemetery, Splain and Wyatt led a procession of about 50 veterans, American Legionaires and family members across Memorial Bridge and past the bronze Italian statues of Valor and Sacrifice that guard its eastern portal. At Constitution Gardens, they were met by a crowd of 150, the sounds of the Navy Band and a round of speeches, the tone of which assured these "forgotten heroes" that they will be remembered after all.

Air Force Secretary Verne Orr, speaking on behalf of President Reagan, remembered the 2.7 million servicemen and women who served during the Vietnam War era, and the 375,000 who were wounded.

"Our military forces in Vietnam served as well as any in our history," Orr said. "They were denied the cup of victory, not because they lacked any of the merits of veterans of earlier wars, but because of the political tenor of the times in which they served.

"They returned home to no parades, no bands, no waving flags. There was no outpouring of public gratitude fo the sacrifices of those who had sweltered in the jungles 8,000 miles from home.Nor was there any outpouring of public sympathy for the families of those who failed to return from those jungles. The United States was sadly remiss. . . . That situation must be corrected, and President Reagan is determined that it will be."

Four seats away from the speaker podium, former radioman Wyatt, who served with the 1st Infrantry Division in Lie Kay, reached down and untied his shoes. So far, $1 million has been contributed to the memorial fund -- $3,000 of it in cash and pledges as a result of his 818-mile hike.

With about $6 million left to go, Wyatt and Splain are riding home.