I have fixed five broken kite boards for myself and mates successfully. There's about three hours of work in it over at least four days depending on how good you want it to look, but every board I have fixed has held and there is no discernable difference in weight or performance. You have to use epoxy resin (polyester resin reacts with the PVC foam). All the materials are available from FGI in Brookvale.
First check the damage. If you bend the board backwards the crease will stand out better to see. You'll probobly see it's creased worse than you thought. Check if the top is cracked. Usually the bottom creases and the top cracks. That's because the bottom is the tensile and the top is the comprssion in the I-beam. If the top is cracked check if the board is twisted or displaced, if it natually returns to it's straight shape. If it does it's worth fixing. If it doesn't it's totaled.

1. Remove all the jump pads, etc. If there is a crack running into a glued on jump pad, remove it with acetone and a syringe, peeling it back with a scraper. Mark the creased section with a texta first. The crease is a section of laminate that has stretched and delaminated. It has to be completely removed. Cut out the section of crease with an angle grinder (flat angle) leaving as long a run-up into the good layers as possible (like about an inch each side). Cut along your marked lines till you hit the foam. (Do this outside, as it makes a mess.) You should be able to lift out the section with a chisel. Also cut through any cracked area on the top at the same flat ange down to the foam. Sand the plastic paint back a couple of inches either side with 60 dry and a block. If you had a one inch wide crease, you would now have about a five or six inch wide section to glass (One inch of exposed green foam, one inch each side of runup into the intact layers and one inch each side of exposed glass), or three inches wide over a cracked section. Hit it with a hair dryer to make sure there is no water left in the green PVC foam. Fill the exposed PVC foam and a bit of the run-up proud with spheres and epoxy resin putty (you mix) using an extra wide scraper. Let epoxy set.

2. Dry sand the filler with 60 grit so your run-up is exposed and check with a straight edge you have a consistant rocker to fill with glass, and refill it if you need to. You don't want to glass over a thin section as this will cause a weak spot. (I-beam principle.) Lay it up stepped with four layers of 4oz glass (or 6-7 layers of 2 oz if you can find it) starting wide where you sanded back the paint and finishing at the outer edge of the run-up section. Blot away any excess resin with a paper towel before it sets; as dry as possible with no air bubbles is the strongest. Even if the top is not cracked, check if the edges are affected onto the top section(delaminated). You might need to wrap one or two layers over the edge onto the top. If you do, pay extra attention that there are no bubbles here before it sets. Let epoxy set.

3. At this stage it's as strong as it's going to be, so check it if it's holding. Bend the board hard. If it's good, continue. Wet sand with 80 grit long strokes. You can cheat the edges a bit. Don't need to get it perfect because you will fill over. Don't over sand. Sand more = prettier result. Sand less = stronger. Fill again proud with the expoxy/spheres putty. Go well over the edges of what you have worked on to get a two inch run up into the raised area so it doesn't leave a visible lump. Make it as proud as possible in the middle. The stuff sands easy, especially wet.

4. Sand with 80 grit wet long strokes with a block. Keep checking your rocker with a straight edge. Refill if you want it perfect. Sand the entire bottom of the board with 120 wet, 180 wet then 360 wet. Dry it well with a hairdryer. Paint the whole bottom with spray can or spray unit if you have one. Epoxy resin has to be painted to protect it from UV. If you know spray painting you can spend a bit of time here to make it look great, finish it with clear, but keep in mind any paint you use (even two pack) is no where near as durable as the plastic stuff they put on it new. One thick coat of plain old primer filler does the job and gives a really good surface for water friction. Plus it's dead easy to retouch. Jump pads reglue with Selley's Kwik Grip.

You can add a whole layer of glass to the bottom of the board as an optional extra step before you paint to make it stronger than new. It adds a little weight and make the board stiffer, but I reckon this flex thing is a bit overrated. They just make these things too damn weak if you ask me. Built-in obselescence, (the light bulb principle, $1100 a pop.).