Since you have water, the easiest would be a big bucket full of water.
That said, if your plastic shower base flexes, this means it was installed incorrectly. These shower bases are quite flexible, so normal practice is to put something between the bottom of the shower base and the floor, for example plaster or mortar, then set the shower base on it. It is then well supported from the bottom. Another reason for your issue may be that the floor itself flexes, but that's less common.
You should first investigate why it flexes. You can do that by kneeling in the shower, setting your weight on the shower base, and looking at the joint between the base and the wall tile.
If the entire shower base lowers by a few mm (ie, it moves vertically and down) INCLUDING THE EDGES then there is a problem with the floor, or the edges are not touching the floor. Since the shower base's edges are its lowermost part, they normally rest either on the floor or on some mortar. If they don't, you have a problem.
If the edges of the shower base do not move DOWN but instead retract towards the inside of the tub, widening the joint gap when you step inside, then the shower base's edges are properly set on the floor but whoever installed it did not put support material below the center of the tub. So it flexes and that pulls the edges in, cracking your caulk.
In this latter case, there is an easy fix: if the empty volume under the shower base isn't too large, you can drill a small hole in the side and inject a can of expanding foam, which will harden and support the shower base from below. Don't drill from the top, of course... that would cause a leak. And don't forget to leave something heavy in the tub while the foam expands... otherwise it will probably lift itself off. Mortar would of course be better, but it's much harder to inject through a tiny hole.