I did some brainstorming with one of my players, and we made a couple of improvements to your numbers.
Wood Elf Barbarian 5, monk 6, wizard 6, fighter 2, Sorcerer 1
Wood elf has base speed 35
barbarian 3 gets eagle totem for dash as a bonus action, barbarian 5 gets +10 speed
monk 6 has +15 speed
wizard 6 gets transmuter's stone for +10 speed, can cast 3rd level spells
fighter 2 gets action surge
Sorcerer 1 gets Wild magic
Feats:
Mobile: +10 speed
Have the magic item Boots of Speed to double your movement speed as a bonus action for 10 minutes max
Since you are level 20 you have access to Epic Boons
Epic Boon of Speed: +30 feet
At level 20 you also have access to Artifacts, which give passive bonuses.
Attuned to an Artifact with a major beneficial property rolled 41-50 gives +10 speed
Base 35
+barbarian's +10 from level 5
+monk's +15 from level 6
+wizard's +10 from transmuter's stone's
+mobile feat's +10
+Epic Boon of Speed's +30
+Longstrider's +10
+Attuned to artifact's +10
x2 from haste
x2 from boots
Turn 1: cast Haste on yourself for the extra action and the double speed
Turn 2: cast Longstrider on yourself.
Click the boots of speed together as a bonus action to double speed again
Turn 3:
Eagle totem or Step of the Wind to dash as bonus action
Move as move action
Dash as Action
Action Surge to dash again
Haste action to dash again
when you've moved your max speed minus your strength score you long jump, going that many more feet, ending at your max speed
while in the air cast featherfall as a reaction, roll 1d20 and trigger wild magic, roll 81 on the wild magic table
Use Wild Magic Free Action to Dash again
The end result of this is 3640 feet in one round, or roughly 414 miles per hour.
Even without the Wild Magic, that's 3120 feet per round, or 355 mph.