Democratic presidential candidate Reubin Askew went to the Florida Democratic convention in Hollywood eight days ago to take up the crown of victory in his home state, but he left with his flanks exposed.

From the beginning, the former Florida governor has been perhaps the darkest of dark horses, an almost invisible candidate who nonetheless has traveled to every state in the union while carefully banking his money in preparation for a media-blitz campaign at the beginning of 1984.

He has avoided the limelight of 1983 while crafting his image as "the different Democrat." But when it came time for his moment in the sun--at a state convention with a straw poll heavily weighted in his behalf--he won fewer than 50 percent of the votes and was grim-faced, even aggressive in victory.

"Wait and see," he told a reporter who asked how he could expect to do well in Iowa or New Hampshire next spring when he could not gain a majority of delegates at his own convention. Then he added quickly, "But I'm sure you'll want to judge it before it starts."

The omens had begun two days earlier on a whistle-stop train trip.

After the first stop, at which reporters and Askew supporters piled off the train to hear the candidate give what his aides had billed as "Trumanesque" speeches, Amtrak's conductors declared a halt to such stops. The triumphant train trip quickly became just another long-haul journey through central Florida.

More indications followed that the weekend would not be all that Askew had hoped for. In Hollywood, it quickly became apparent that organized labor was making a major effort for former vice president Walter F. Mondale, and on Saturday, Oct. 22, the rhetorical battle that stirred the hall was between Mondale and Sen. John Glenn (D-Ohio), with Askew's speech a trailer.

The next day, hours before the straw poll, three Florida newspapers published a poll showing that Mondale, not Askew, was the favorite of state Democrats for the nomination, by 32 percent to 26 percent. Glenn was third with 19 percent.

More importantly, the poll emphasized the problem faced by Askew in a state that has grown rapidly in the years since he was first elected governor in 1970. Among those who remembered his successful tenure as governor, Askew was the overwhelming choice for the nomination; among those who have lived in Florida for six years or fewer, Mondale beat him handily.

"I've said from the beginning that Florida's a big state and that we estimate that some 3 million or so people have moved in since I was governor," Askew said. "And while I do very well with those who know me the best, I mean, I've got a challenge to present myself as a presidential candidate to the rest of the state."

Jim Krog, Askew's campaign manager, said the poll only confirmed what the candidate knew.

"We need to do some television in Florida for those new residents," he said. "But it also confirms that we had a base in Florida and that base still exists. Among 39- to 45-year-old Democrats, we blow them the other candidates away."

Askew's campaign strategy is simple.

"We hope to do better than expected in Iowa," said press secretary Jim Bacchus. "We hope to do even better than that in New Hampshire. In doing so, we hope to establish the credibility we need to do well on Super Tuesday March 13 , especially in the southern states of Georgia, Florida and Alabama."

To accomplish this, Askew plans a media barrage, financed mostly by the almost $1 million in federal matching money for which he has qualified. "We're the only solvent dark horse," Askew said.

Some of that advertising effort has begun. A film made by Eli Bleich, a Hollywood, Calif., media consultant, is in circulation in Iowa. This past weekend, Askew planned to begin running advertisements in Florida, based on the state convention. Around the first of next year, a more intensive media campaign is to be launched.

"I've got to go directly to people and talk to them," Bleich said. "I've got to get beyond the press."

Askew's message in this campaign is a combination of his record as governor, where he was judged to have been highly successful, and his willingness to tell elements of the Democratic Party things they may not want to hear. He recently stepped up his attacks on Mondale as a captive of special interests and is likely to confront Glenn on the same issue.

"I'm tough to discourage," Askew said after the straw poll. "I'll tell you what, I've run uphill most of my life. It isn't so much what people say in straw polls, it's what they say when they vote. I'm a risk-taker . . . . I'm not looking for guarantees. I know it's hard work."