I was in the thick of that particular campaign, actually. It was not a wipeout by any means, but not a very close run thing, either. If John Cornyn had made some sort of massive mistake (on the scale of Clayton Williams in 1990), Kirk could have had a good shot at winning.
As far as African-American candidates go, he had the best chance of any in Texas, as his tenure as Dallas Mayor showed that he was no radical leftist and was quite capable of getting on well with business interest. Nopr was Cornyn particularly well known.
Kirk's strategy was to win big on his own turf in Dallas as well as in the Democratic stronghold of Austin, split the vote in San Antonio, while holding down Cornyn's vote in Houston and the rural areas. Alas, the color of a man's skin was still a factor to too many voters in the Lone Star State, and he went down to defeat.
A Kirk victory would have had a substantial impact on Texas politics. After 1994, the Texas Republicans gained a major talking point by the fact that they held every statewide office in Texas. This played a major role in convincing the media and the public that Texas was as Red a state as one could get. With a Kirk victory, the Republicans cannot claim this and the fundamental situation in Texas politics becomes a bit more fluid. A statewide Kirk constituency also helps maintain the organizational strength of the Texas Democratic party, which faded abdly after 1994 IOTL.
Kirk for Governor in 2002?