Disclaimer: May not work for everyone. Just sharing my lived experience as someone who runs with absolutely flat feet.
I've been living with absolutely flat feet and severe Achilles tendonitis for over 3 years and I even have bone spurs now (extra growths of the heel bones) on both ankles.
I've been a barefoot runner for over 5 years now and that fixed my knee pain and strengthened my calves. However, I started jumping rope barefoot on concrete :( about 4 years ago and I did that for a year and it messed up my Achilles! (Don't ask why! I thought I was being a Spartan :D)
So bad, that of late I have been hobbling out of bed in the morning and I'm 45 years old so that's not fun at all.
Recently, I discovered something interesting by chance. If I work out in the gym with heavy weights in the morning, even for something so upper body-ish like just shoulders, I don't limp for the rest of the day.
Basically, one day I limped to a gym as I was travelling and didn't feel like running in a city without pavements (common in India). I did chest that day and while walking back, I realised I wasn't limping anymore.
Read up a little about this effect and one possible explanation is exercise-induced hypoalgesia.
It works so well that on Sunday, I completed a half marathon barefoot and was hobbling so badly the whole day that I just lay in bed. Monday morning the pain was still bad in both feet and I didn't feel like doing anything at all, but I pushed myself to the gym for an upper-body workout (only shoulders). Had to ask someone to drop me to the gym though it's just a 100m away.
Voilà! Achilles pain gone.
And today's Tuesday morning. Just got out of bed. Feeling great, so sharing this with everyone.
Not saying that disappearing pain means the tendon itself has magically healed. I'm sharing this because the difference in how I feel after a proper gym workout has been dramatic and consistent!
Hope this helps!