ffmpeg recoded mp4 files error on mobiles in Video JS - ffmpeg

Question

We are converting seriously old .flv files to MP4 with FFMPEG. These are at least 10 years old.
Back then all were rendered with early versions of Adobe Premiere.
On desktop browsers all the files work and stream (...watching them feels like going back a century!)
But when requesting the videos on the same pages on mobile devices (android and ios) Video JS doesn't even show up.
Perhaps the codec is just too old, but I was wondering if there could be another reason when converting them with this line:
for i in *.flv; do ffmpeg -i "$i" "${i%.*}.mp4"; done
If not, is it possible to detect this in Video JS, so we can show an announcement that the video is only visible on desktops?
I hope someone here has this knowledge!
added on request of llogan
ffmpeg version N-78967-gbaec6d8 Copyright (c) 2000-2016 the FFmpeg developers built with gcc 4.8.5 (GCC) 20150623 (Red Hat 4.8.5-4) configuration: --prefix=/root/ffmpeg_build
--extra-cflags=-I/root/ffmpeg_build/include --extra-ldflags=-L/root/ffmpeg_build/lib --bindir=/root/bin --pkg-config-flags=--static --enable-gpl --enable-nonfree --enable-libfdk-aac --enable-libfreetype --enable-libmp3lame --enable-libopus --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libx265 libavutil 55. 19.100 / 55. 19.100 libavcodec 57. 28.100 / 57. 28.100 libavformat 57. 28.100 / 57. 28.100 libavdevice 57. 0.101 / 57. 0.101 libavfilter 6. 39.102 /
6. 39.102 libswscale 4. 0.100 / 4. 0.100 libswresample 2. 0.101 / 2. 0.101 libpostproc 54. 0.100 / 54. 0.100 Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'a_4293_06.mp4': Metadata:
major_brand : isom
minor_version : 512
compatible_brands: isomiso2avc1mp41
encoder : Lavf57.28.100 Duration: 00:01:40.10, start: 0.023220, bitrate: 492 kb/s
Stream #0:0(und): Video: h264 (High) (avc1 / 0x31637661), yuv420p, 320x240, 376 kb/s, 30 fps, 30 tbr, 15360 tbn, 60 tbc (default)
Metadata:
handler_name : VideoHandler
Stream #0:1(und): Audio: aac (LC) (mp4a / 0x6134706D), 44100 Hz, stereo, fltp, 123 kb/s (default)
Metadata:
handler_name : SoundHandler At least one output file must be specified

Answer 1

Thanks to #llogan's comments I can answer this one myself.
First, I upgraded ffmpeg to the latest version, and then did some research on the -movflags and +faststart.
I found a 2015 article with great info on how to convert .flv to .mp4 (https://addpipe.com/blog/flv-to-mp4/)
So, in order to make the new .mp4 files compatible with mobile devices, you need to add a profile and a level, like this:
in a batch convert:
for i in *.flv; do ffmpeg -y -i "$i" -movflags +faststart -profile:v baseline -level 3.0 "${i%.*}.mp4"; done
and for a single file:
ffmpeg -i filename.flv -movflags +faststart -profile:v baseline -level 3.0 filename.mp4
And then the terminal shows this line when converting:
Starting second pass: moving the moov atom to the beginning of the
file
That is needed, but the addition of the -profile and -level actually made the videos work on the mobile devices.