Flare Statistics for Young Stars from a Convolutional Neural Network Analysis of $\textit{TESS}$ Data

All-sky photometric time-series missions have allowed for the monitoring of thousands of young ($t_{\rm age} < 800$Myr) to understand the evolution of stellar activity. Here we developed a convolutional neural network (CNN), $\texttt{stella}$, specifically trained to find flares in $\textit{Transiting Exoplanet Survey Satellite}$ ($\textit{TESS}$) short-cadence data. We applied the network to 3200 young stars to evaluate flare rates as a function of age and spectral type. The CNN takes a few seconds to identify flares on a single light curve. We also measured rotation periods for 1500 of our targets and find that flares of all amplitudes are present across all spot phases, suggesting high spot coverage across the entire surface. Additionally, flare rates and amplitudes decrease for stars $t_{\rm age} > 50$Myr across all temperatures $T_{\rm eff} \geq 4000$K, while stars from $2300 \leq T_{\rm eff} < 4000$K show no evolution across 800 Myr. Stars of $T_{\rm eff} \leq 4000$K also show higher flare rates and amplitudes across all ages. We investigate the effects of high flare rates on photoevaporative atmospheric mass loss for young planets. In the presence of flares, planets lose 4-7% more atmosphere over the first 1 Gyr. $\texttt{stella}$ is an open-source Python tool-kit hosted on GitHub and PyPI.