Me and my best buddy play this matchup all the time (I main Kag and he mains Haz), so I hope I can have some decent input here. I would argue that the matchup is tough, but by no means free for Hazama.
-Important principles-
-Never jump in on him in neutral
-Orbs are killed by snakes
-Backdash at match start unless you're confident they'll jump, in which case 6C for a free combo that can end with oki
-If performing a combo that usually ends with 5DC or flash kick, switch it up in a way that keeps him grouded so you can keep him locked in okizemi - letting Haz do anything is a pretty bad idea
A lot of Hazama's pressure (the guy I play against anyway) tends to include stance moves, and these are easily punishable by a flash kick and to pick up a short combo if you score a counter hit. Of course, this will only work once or twice until they're conditioned to stick with safer options. It's at this point I start feeling more comfortable in throwing out C normals to fish for counter hits. It's important to bare spacing in mind at all times because Hazama's middle-distance game sucks pretty hard, and Kag's pokes outrange Haz's by quite some distance, so feel free to throw out a 5C or 2C if you're at the safe range.
Another pattern I noticed is with Hazama players pressuring with snakes in mid-screen (5D~A, 5D~A ad infinitum). These players are clearly NOT familiar with the matchup, because if you make use of 6DC's projectile invulnerability and predict the snake's timing right, you can easily score a counter hit and pull 5k out of the bag without any trouble, once again limiting Haz's middle-distance options severely. Don't be too reliant on it though, as a well timed Rising Fang from Haz will completely shut down a 6DC.
Predicting his chain jump-ins is a totally different matter, but a preemptive 6C, while risky as hell, can score big damage if you know the timing for the 6DB follow-up well enough - an easy 4k punish for something as critical to Haz as a jump/chain in. Again, spacing is important here because 6C has an absolutely RIDICULOUS hitbox, covering a massive area in a relatively short time. Your only problem is the slow startup. 5DC is another option but again the recovery leaves you really vulnerable if you mess up. It's also possible to meet a chain-jumping Hazama with a super-jump j.C, but the timing is pretty tight so don't bother unless you're really confident you'll hit him.
This is the same for most any matchup, but once you have your opponent in the corner and you know they like to mash out of pressure then try to include 5DA in your block strings - the super armour will almost always score you a counter hit that you can follow up with decent damage, provided you time it right. Again in the corner, end EVERYTHING with orb okizemi, ESPECIALLY with Hazama because of his easy ways to escape the corner with chains.
Mostly though, it's about patience. Don't try to do drive strings on block, especially if he has 50 meter to spend on a houtenjiin. Just wait for punish opportunities, because there will be plenty of them.