The Zambians were the stronger of the two sides, particularly in the first half, but could not convert the pressure into goals.
The Chipolopolo head up the table with four points from their two games, after beating Djibouti 3-0 on Wednesday.
Kenya have only two points, following their second successive 0-0 draw, having also been held by defending champions Sudan.
Kenya coach Francis Kimanzi, however, remains confident of his team's chances of making it to the semi-finals.
"We have had a slow start but when you look at the level of opposition we have faced here, then you see we still have a chance," he said.
"I cannot sit back and relax at this point. The road ahead is tougher so we can only pray that we win the rest of the matches," he said.
Burundi kicked off their campaign by easing to a 4-0 win over Djibouti in Jinja, Uganda, to put them second in the group.
Eric Gatoto and Claude Nahimana each scored twice to send Burundi on their way.
Djibouti suffered a further blow in the dying minutes when Mohamed Merane was sent off by referee Ally Kalyango for rough play.
On Saturday, Somalia play their first game in two years when they take on Tanzania, while hosts Uganda meet Zanzibar.
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