FFMPEG - Use drawtext and complex filters
Just chain the drawtext, at the end.

ffmpeg \
-i video1.mp4 -i video2.mp4
-filter_complex "[0:v:0] [0:a:0] [0:v:1] [0:a:1] concat=n=2:v=1:a=1 [v][a];
[v]drawtext=text='SOME TEXT':x=(w-text_w):y=(h-text_h):fontfile=OpenSans.ttf:fontsize=30:fontcolor=white[v]" \
-map "[v]" -map "[a]" -deinterlace \
-vcodec libx264 -pix_fmt yuv420p -preset $QUAL -r $FPS -g $(($FPS * 2)) -b:v $VBR \
-acodec libmp3lame -ar 44100 -threads 6 -qscale 3 -b:a 712000 -bufsize 512k \
-f flv "$YOUTUBE_URL/$KEY"