Wait.. so the waste is supposed to flow out of the disposal and then in to the flex pipe and go up in to the main drain?
If that is what is happening then that probably explains why there is a leak. Water drains by gravity. The purpose of the trap is to hold water to prevent sewer gases from coming up. After that you need to have the pipe go downward at 1/4" slope per foot to tie in to the drain. So you need to find a way to move it down, not up.
I've been told here that flex pipe is not very good to use in general, but having it on a garbage disposal is really not a good idea because it will likely catch the gunk that goes through it.
Is it the drain for a sink that it is tying in to? I can't really tell. Maybe you can lower the height of whatever it is connecting to so that you can have it go at a slightly downward slope.
shows some common mistakes when installing a garbage disposal unit.
Here is an example of how a double sink with disposal is plumbed:
Flex pipe is not approved for use by UPC, if I recall correctly.
(I'm not a plumber, just a DIYer who has been studying the plumbing code and trying to learn from the pros here).