Eh, Kayle isn't all too great at physical DPS. The main part of the reason is that she doesn't have any abilities that benefit from her physical damage except for Righteous Fury, and from what I understand, you can't boost that through physical damage items. The other reason is that Kayle is a terrible farmer and relies on champion kills to get gold.
You can "keep" her healing and protection abilities, she never loses them. :-P In fact, Intervention gets no boosts from items. Divine Blessing, her heal, gets increased healing from AP but the AP ratio on it is not good (AP*.6)
You'd be able to make Righteous Fury better by increasing her attack speed, which would also boost her DPS. Another important thing about Kayle is her chasing abilities. She can slow down enemies with Righteous Fury, increase her speed with Divine Blessing, and use Intervention to tower dive. So, you should try to put some emphasis on that, too. Kayle's healing is actually pretty bad and only useful in the laning phase (the only character who has a team heal that is useful past the laning phase is Soraka) and for increasing someone's speed.
-Wit's End: Attack Speed, Gives you MR, too.
-Zeal: Gives you Attack Speed, Critical Strike, Movement Speed, and is cheap! You might get away with stacking it, too...
-Phantom Dancer: Expensive, but gives you Attack Speed, Critical Strike, Dodge, and Movement Speed.
-Sword of the Divine: Gives the highest boost to Attack Speed, and keeps with the "theme" of doing both magic damage and physical damage that Righteous Fury gives you due to it's passive. It's active + Reckoning helps you take down other physical DPS
-Boots of Swiftness: Some would say Berserker's Greaves, but Swiftness gives you more speed during a chase. Berserker's Greaves is a decent choice, too, though.
-Negatron Cloak: Some people would deride me for recommending an item that gives you nothing but MR, but it's cheap and along with Wit's End, brings you to the soft cap of 100 for MR to deal with casters.
-Nashor's Tooth: +30% Attack Speed, Mana Regen, 55 AP, and 25% Cooldown Reduction gives Kayle a little bit of everything she would need. Stinger does almost the same thing except less for a cheaper price.
If I were to theorycraft a physical based Kayle on the spot, I'd start with Righteous Fury, get one point of Reckoning just so I can chase, get a couple of points in Divine Blessing for the laning phase, get Intervention every time, and try to make Righteous Fury as strong as possible.
Get a Doran's Ring first so you won't ever die unless you are the only target of harassment and you get mana regen, and a small boost to your abilities. Get maybe an Mana Pot. Harass often with Righteous Fury and Reckoning, but don't bother chasing unless you have a competent lanemate.
Then, you should probably get a Dagger to build into Berserker Greaves, Zeal, Sword of the Divine, Stinger, whatever you want. Boots would be good, too, and then you can get Boots of Swiftness or Berserker Greaves.
Then you get an attack speed item, and once you get Intervention, try to start ganking. Kayle relies on champion ganking, and if you can't gank, you will lose. She can't stay competitive by farming (she can't farm well), so spam Righteous Fury and kill, kill, kill.
Also, one more thing: most builds are technically viable on Kayle, because she's a weird, balanced character. But it doesn't mean it will be good.