I have Leonin Shikari on the board and want to equip a creature. Can I activate the equip ability a second time and put it on the stack? Like when giving a creature hexproof with an equipment, and an opponent casts a spell to destroy the creature before it gets hexproof, can I activate the ability a second time to have it on the stack above their spell?
You can activate the Equip ability any time during your Main Phase, when you have priority and the stack is empty.
702.6a. Equip is an activated ability of Equipment cards. "Equip [cost]" means "[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery."
With Leonin Shikari on the board, aren't limited to activate it during your turn when the stack is empty (so not just "when you could cast a sorcery"). This means you're allowed to activate the ability in response to a player's attempt to remove one of your creature with a targetted spell.
Because the stack resolves last-in-first-out, your Equipment will be attached to the creature of your choice in time to give it Hexproof before the removal spell resolves. That spell will be countered by the game rules ("fizzle") for not having a legal target anymore.
608.2b. If the spell or ability specifies targets, it checks whether the targets are still legal. (...) The spell or ability is countered if all its targets, for every instance of the word "target," are now illegal. (...) Illegal targets, if any, won't be affected by parts of a resolving spell's effect for which they’re illegal. Other parts of the effect for which those targets are not illegal may still affect them. (...)