I can think of two:
- Heel front kick. As @Sean Patrick Floyd said, it's more of a thrust kick
- Toe front kick. Basically, you will kick straight in, with your toes into the target. The target, in this instance, is the abdominal waist band muscles. The direction of the strike is in and down.
I do not recommend the toe front kick lightly - for most people who aren't trained that way, it's a great way to break toes. Play with it a little, very lightly, and experience for yourself the amount of flexibility and pain that you have.
@THelper recommended sitting in seiza for a while - not a bad way to increase flexibility, but it sounds like what you need is actually sitting for a while, moving your toes up and down, maybe isolating one and moving it with your fingers (gently, of course!) while exercising the muscles (gently, of course!). After a few years, you might get an improvement. The body DOES change based on what you ask of it - but bone changes take a long, long time.
An art like taichi, done properly, is very good for any and all flexibility. Working the entire body takes the boredom out of focusing on solely your toes, and you might get results at the same speed or faster.
Or not. Your mileage may vary.
Hope this helps.