I have a somewhat unique front tuck in that I block with my hands behind me as opposed to above my head.
It's called a Russian lift/blocking technique. It's actually almost similarly as powerful BUT it is harder to do double fronts and combination skills out of it... of course, on hard ground (grass, concrete, etc.) if you can do front skills connected that is pretty godly anyway.
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The guys before me covered pretty much all of what I am going to say although I will rehash it and elaborate a bit more. Your lack of jump is related to your technique, not your jumping ability.
1. Your block (jump) is pretty poor. Get FULL arm extension from your hands... basically you want to extend them all the way. The way I like to teach a proper front tuck is to basically make you look UP and throw your hands straight towards the ceiling. This will prevent you from tilting your torso forward which ultimately kills your jump, and to get full arm extension. Take your jump to its apex then tuck tight and you will find that you can basically float out of tucks easily instead of landing in a squat.
2. Angle of takeoff is poor. As you can see, your forward momentum is basically taking you from in front to the mattress to beyond it which is like 5-6 feet if not more. This is NOT good. Preferably you should only be traveling 1-2 feet forward to maximize height. This kind relates to point 1 in which you are dropping your head and tilting your torso forward as you jump. This will get you over BUT the flip will obviously be pretty close to the ground which is not very good. Keeping your head up and looking to the sky will help to prevent this when you make your block.
3. Tuck needs to be tighter. Work on ab exercises to strengthen your core and do explosive tuck jumps on the ground. This will also help your back flips as well.
Standing fronts on flat ground are relatively easy if you have a good front tuck. I haven't tried them outside in a while, but I've been able to standing fronts up onto 1 ft mats in the gym. It's pretty cool. Um, I wouldn't suggest trying to learn these until you have a solid, SOLID front tuck though.
You HAVE to recognize the power that comes from the hands and the extensive heel drive you get from an explosive tuck though. Basically you're standing on the ground with your arms up straight overhead in a bit of a hollow position. Arms bend at the elbows as the hands drop behind your heads while at the same time you rock your body from a slightly hollow position into a slight arch. Then from there, it's full go of your hands accelerating and your lift is going to come mostly from a plyometric moment of your toes pushing into the ground with your calves and the extension of your body into the tuck.
