What would be the purpose? In other words, what would you do with the information? The amount of flexing is only indirectly related to potential beam failure so displacement data alone wouldn't tell you much.
Vibration data (displacement changing at moderate frequencies) are readily obtained with your very own, built-in human sensors -- no electronics needed.
We have 180-year-old floor joists that some $%#@ local yokel electrician cut half-way through, in the middle, from the bottom to install electric oven and AC wiring in the early 1980's. Solution to flexing of the floor was to repair the joists. When we moved in a 900 lb table to the dining room, the solution was to add support in the crawl space. In other words, 'assess and address' -- no 'monitoring' needed.
My 2 cents ... Marc Marc_F_Hult