Leaking whirlpool tub; in alcove, but no tile flange at bottom of walls
If you clean the old caulk off, properly prepare the joint, use 100% silicone caulk ,and your tub or walls do not move more than they are suppose to (natural flexing is ok), then you should have no problems with water at the caulked joint.

For best results, fill the tub with water before caulking, and keep the tub filled until the caulk is completely dry. This will open the joint as much as possible and then leave it under compression.

If it is flexing too much and that is breaking the caulk (you mentioned it but 100% silicone should be able to flex a lot), then maybe remove the tub and reinstall with a proper mortar base.  If it still moves too much is the floor structurally deficient?