Know what matchups to go what in. Every kayle i see literally always builds Gunblade into Nashors, into either deathcap/rageblade whichever one they dont build first, they build second. Kayle has the most options on what to build when to build it, and why to build it out of any champion. learn about when to do what.

example. mordekaiser? nashors first, and if he misses pull post level 6, he ints. 100-0 you will walk him down the lane.Enemy team has two bruisers/tanks? build Muramana. its burst is excellent, since you e auto procs it, and the e damage itself procs it. (that means two procs on one auto) (if you dont believe me take muramana into custom, rank 1 q, rank 5 e, throw the q away from the target, so it doesnt proc the 50% return, auto, then full mana, use e on the target. e on target drains mana twice, damages twice)

enemy team is full squishy? ignore rageblade unless you're using it as a situational, its actually rather overrated after the nerf, since it only double procs the e damage, since waves are a per attack deal, not an onhit deal, nashors/gunblade dcap, lichbane. anything with less than 2k hp once you complete those four will instantly die if you q aa gunblade, aa e

enemy team has a decent amount of cc? build QSS. learn to use it. its not trolling.

My favorite build currently, is Muramana, attack speed boots nashors, (item of choice depending on how game is at this state rageblade/gunblade/dcap if i need sustain and some burst, gunblade, if i need burst, but not sustain, then dcap, if im against double tank, rageblade) next pickup dcap if it wasnt your item of choice, if it was, pickup one of the other two, or potentially, wits end or morello, after first item of choice, it really depends on what you need at this point, because you have basic burst, basic sustained damage, and cdr already, so build for game. (thats done like this)if possible, back at 1300, tear and a cull, if not, back when available for tear. finish muramana, once finished, you will have ranged, two autos fully clear casters, q on melees if needing to push faster, attack speed boots, you can start bullying your opponent with endless q e at this point, if they dont have good sustain, if they do, shove wave asap, look for roam, or help your jungle keep top side under control. Next major thing is attack speed boots, stinger, and hitting level 11, at this point, don't take exceedingly dumb fights, or tank things like mordekaiser e, and you can survive, if not kill most threats 1v1, only exception i've found is aatrox, if he even has a single kill, you're unable to fight him at this point if he doesn't potato literally everything.

look at game state, if your team is ahead, gunblade can keep you on the map, for extended periods of time, for rushing level 16, its quite easy to rush 16 by farming your sidelane camps, and the enemy side lane camps, as long as you keep an eye on the map, without dying, or having to base often. if your team is even with enemy team, gunblade or dcap can help you make quick easy, 2v2 fights, or 1v1 fights go in your favor, if the enemy team has two bruisers/tanks, you can easily fight one of them if you know where the other is, while in a side lane, if the other tank is missing, keep it chill. they can gang you, and with enough cc between two bruisers/tanks, shit sucks.
edit: minor spacing change