In my experience you probably need clamps. Try some veneer glue instead, I use "cold press" titebond, bu the pros like Paul swear by hide glue.
There are recipes for veneer flattener out there. You just spray the wood (old windex bottle is what I use) then set it between a pair of flat boards (I use 3/4 melamine) and place paper towels/newspaper on each side of the veneer then the board. Weight it down good and change out the paper a few times during the first few hours as they get damp.
A day or so later it should be much flatter and you need to do the veneering before the stuff decides it wants to become a New Mexico highway again.
I apply the glue with a 4" ink roller to get a good wet surface, just like a layer of latex paint. Some substrates really like to soak it up so you may need to wake a few minutes then apply a little more and spread it out. I like to place a layer or two of paper towels between the cauls to suck up any squeeze through.
I use a vacuum bag, but you can get good PSI on smaller pieces with a few more thicknesses of flat cauls (prevents distortion from the point loads of the clamps) and squeeze it tight, edges and center, with your strong clamps (parallel jaw and "F" style can really put the force into it.
The cold press glue takes about 2 hours to set up before you unclamp. Set the board out so air can get to each side, this lets it dry evenly and avoid warping.
You do need to balance the veneer on both sides at once.