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We present an expansion of FLEET, a machine learning algorithm optimized to select transients that are most likely to be tidal disruption events (TDEs). FLEET is based on a random forest algorithm trained on the light curves and host galaxy information of 4,779 spectroscopically classified transients. For transients with a probability of being a TDE, \ptde$>0.5$, we can successfully recover TDEs with a $\approx40$\% completeness and a $\approx30$\% purity when using the first 20 days of photometry, or a similar completeness and $\approx50$\% purity when including 40 days of photometry. We find that the most relevant features for differentiating TDEs from other transients are the normalized host separation, and the light curve $(g-r)$ color during peak. Additionally, we use FLEET to produce a list of the 39 most likely TDE candidates discovered by the Zwicky Transient Facility that remain currently unclassified. We explore the use of FLEET for the Legacy Survey of Space and Time on the Vera C. Rubin Observatory (\textit{Rubin}) and the \textit{Nancy Grace Roman Space Telescope} (\textit{Roman}). We simulate the \textit{Rubin} and \textit{Roman} survey strategies and estimate that $\sim 10^4$ TDEs could be discovered every year by \textit{Rubin}, and $\sim200$ TDEs per year by \textit{Roman}. Finally, we run FLEET on the TDEs in our \textit{Rubin} survey simulation and find that we can recover $\sim 30$\% of those at a redshift $z <0.5$ with \ptde$>0.5$. This translates to $\sim3,000$ TDEs per year that FLEET could uncover from \textit{Rubin}. FLEET is provided as a open source package on GitHub https://github.com/gmzsebastian/FLEET