As with most things 5e’s approach to swimming in armor is let it happen unless there’s a rule against it. And people wonder why 5e has an “Easy Mode” reputation.
So swimming in plate mail? I allow it – i assume you are going to sink 1′ per 1 second
Nekked (sinks 0′ per round)
Clothing (sinks 1′ per round)
Light Armor (sinks 2′ per round)
Med Armor (sinks 4′ per round)
Hev Armor (sinks 6′ per round)
Athletics check (DC10) whatever your result is above 10 is the number of feet you can move in a round. If you get a 16 you can either tread water for the round (eliminating the 6′ of downward movement) or move forward 6′ and sink 6′ – Say you roll a 20, have athletics (+3 for prof), and (+4 for strength) – I’ll let you move 17′ (again -6 if you want to stay afloat)
If you have more than you need (for example got 17 but only need 6 to tread water) i’ll let you add whats left to the next round.
After 1 minute make a DC(1) constitution check. After 2 minutes make a DC(2) constitution check etc. A failed constitution check adds 5 to the athletics checks and the con checks start back at one.