Also, I don´t believe silica gel "soaks up" methylamine gas
Calcium chloride will definitely absorb the methylamine or any amine. I would be wary of silica also. NaOH pellets would be best for drying methylamine gas. Bubbling the methylamine gas through a saturated NaOH solution should also work. You can even get away without any drying if you let the gas cool through a long neck flask or reflux condensor.