Had another few chances this last week, not cycling related, to find out from the "horses mouth" as it were, what they'd look for. Both paramedics at the scene(if you weren't making much sense/confirm details given) and at A&E's.
Both seem to favour medicalert or similar. Keeping it simple, laminated card as suggested by @
Cunobelin. Name, address, Dr's details & hospital number on one side, any medication and allergies on the other.
Whilst they can look at your phone, it requires two people(It's got that bad). If in use on the bike, they may not bother looking at it. "They're there to treat the person." Whilst they're looking at your phone, whose looking after you.
Items of clothing may be cut and or removed, helmets included, at the scene.
Edited to read
"Items of clothing may be cut and or removed"
from
"Items of clothing may cut and or be removed"
AskMid roadside Service
http://m.askmid.com/mt/www.askmid.com/mobile/
& PC/tablet
https://ownvehicle.askmid.com/