Chechnya was an autonomous republic, think province or state with more privileges, within the Russian SFSR while Ukraine, Kazakhstan, etc were "independent" republics in the Soviet Union.

Another example is within the Ukraine SSR; the Crimea declared itself an autonomous republic in January 1991 & stayed with Ukraine during her independence movement.

Source: The Last Empire - Serhii Plokhy

As noted, Chechnya was an autonomous republic within Russia, while places like Ukraine and Kazakhstan were full union republics in the USSR, and as such were technically allowed to secede under article 72 of the 1977 constitution. As an autonomous republic Chechnya was not given such a right (not that it was really a factor).

As well it should be noted that initially there was little done to keep Chechnya within the newly formed Russian Federation. An initial attempt by Russian forces in 1991 failed to restore Russian control over the region, Chechnya was de facto independent, and maintained that status until 1994.

This changed because of skirmishes along the de facto Chechen-Russian border and just the general lawlessness that came from an unrecognised state with no strong government control. Russia moved to reassert its control over the region, and thus began the First Chechen War.