I have combined 4 Might as a Rengar player and I want to play Kinkou Initiate. Can I draw a card with using Rengar ability or is this ability after I played a card?

Yes, you can draw. Both abilities trigger at the same time ("When you play a unit" / "When you play me"), and since you control both, you choose the order they go on the chain (Rule 333.1).

Put Kinkou Initiate's draw trigger on the chain first, then Pridestalker's +1 Might on top. The chain resolves top-down, so Rengar's buff lands first — bumping one of your other units to push their total to 5 — and then Kinkou Initiate resolves and checks "your other units have total Might 5 or more" at that moment. That check happens on resolution, not when the card was played, so the buff counts and you draw 1.

Note Kinkou Initiate checks your other units only — its own 3 Might doesn't count toward the 5.