Saddam was a paranoid control freak with a police state along Soviet lines. Those types of dictators don't tend to want to arm up anyone they can't directly control, they don't tend hand out heavy weaponry willy nilly to loose cannon types. There's really no evidence that he was closely aligned with radical islamist groups. He was leader of a state based on conventional armed forces, actively fighting
against radical islamists for most of the time period that matters. The idea that Saddam would e.g. build nukes then hand them out like christmas bonuses to roving bands of lunatics really defies the logic of why all heavily centralized states make nukes: not to use them, but to say "bugger off! I got
nukes buddy!" Giving nukes away to loonies sort fails at being a deterrent, because it causes you to be more likely to be attacked rather than less. If he had a few nukes, he wouldn't be secreting them off to random nutters, he'd be stockpiling them to use as a diplomatic club to threaten people with.
Iraq and Saudi Arabia actually had
extremely close relations in the 1980's due to mutual fear of an Iranian-style islamist revolution spreading, with Iraq getting a significant amount of aid from the Saudis to fight against Iran. Saddam was getting aid from both the USA and USSR at the same time too. If Saddam was doing stuff that would destabilize any of his benefactors that wouldn't go unnoticed, and would jeapardize the military aid that kept Iraq alive against Iran.
Tying this back to the USA, USA did in fact have an official program which was
arming up islamic terrorists in Afghanistan to fight the Soviets.
Osama bin Laden was amongst these people. Since Iraq in the 1980's was receiving massive amounts of military aid from
both the soviets and the americans during the Iran/Iraq war, it doesn't make a lot of sense that he'd be amongst the sponsors of these groups, which evolved into Al Qaeda in the 1990s.
Note that America was secretly arming up both Iraq and Iran with heavy weapons (AA and anti-tank) but also prohibited chemical weapons to
both sides (see Time magazine, the guardian articles I linked) during the Iran/Iraq war (anything to make a profit I guess, the USA are like the Pherengi, but more deadly), plus created the networks of saboteur training camps in Afghanistan which later became Al Qaeda. Thanks for doing all that, guys.