Some things to note.
1) Rush the hextech gun blade first because ur only going to have lvl 1 heal to stay in the fight and u need the life steal.
2) Always get the AD before the AP part of an item.
3) GA is very optional. Depending on the game consider getting another blood thirster or a banshe veil.
4) In some condition consider getting a second vampiric scepter rather early if you dont want to have to go back to base.
5) Use the 35 gold pots for health often early game. Maintain enough mana so u can Q blast and deney ur enemies.
6) Start witha meki pendant or the safer but longer route and get a doran's ring.
7) Cleanse is not nessacary and some games u will rather want exhuast or flash.
8) At level 11 or so kayle has the hardest ranged auto attack in the game pretty much... go kill people and make them QQ b/c they thought kayle was worthless hero.
9) Last point is even tho kayle is a DPS hybrid I would not play her on a team that already has 2 hard carries already. Taric is much better suited for that position.