A character can use Dash multiple times, given the actions to feed them. The Speed limit doesn't prevent multiple Dash actions and using their granted movement, as exceeding your Speed in a defined way is explicitly what Dash does.
That's not why the Amazing Lightspeed Horse doesn't work. There's no conflict between those two answers.
The reason the Amazing Lightspeed Horse doesn't work is because it's not using multiple Dash actions. It can be ordered to Dash by as many riders as one might like, but it still can't execute such an order when it has run out of actions (bonus or otherwise) with which to Dash.
Pre-empting the counter-arguments
“But a mount uses its rider's actions.”
A mount doesn't use its rider's actions. A controlled mount uses its own actions to execute the rider's directions (PHB p. 198, emphasis mine):
It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge.
So the poor horse getting an infinite number of riders is still limited by its own allotment of actions no matter what blizzard of orders it is bombarded with.
“A mount gets a new turn and new actions for each new rider.”
It's true that a mount gets new actions on a new turn, but the mount isn't getting a new turn with each new rider in a round. Controlling a mount only makes the mount to use its (singular) turn for the round synchronously with the rider's turn. The following is the entirety of the rules creating this concept of overlapping turns, and it can't be read as creating a fresh turn for the mount (ibid):
The initiative of a controlled mount changes to match yours when you mount it. […] A controlled mount can move and act even on the turn that you mount it.
Swapping infinite riders doesn't give the horse infinite fresh turns and the fresh actions that would in theory come with those turns.
Thief's Reflexes ability
Yeah, this works. A 17th-level thief who gets two turns in the first round of combat gets all the actions they can execute. There are two things to consider:
Can you move your Speed on each turn, or just once because it's one round?
You can move your Speed on each of the two turns, as defined by the core Movement and Position rules (PHB, p. 190):
On your turn, you can move a distance up to your speed.
Can you Dash multiple times?
As many actions as you have to devote to a Dash action each turn can be used to Dash. For a Thief with Thief's Reflexes and Cunning Action, that means a total of 4 actions (2× Action, 2× Bonus Action) could be devoted to increasing available movement over the course of the two turns.
As a result, two turns in one round makes for being able to move Speed feet twice and adding Speed feet to available movement four times, for a total available movement over those two rounds of 6× one's Speed.