Dash is an action that can be taken by any character, and by some as a bonus action, and Tabaxi's racial feature feline agility can be used as part of their movement, not action or bonus action.
So a tabaxi's base speed is 30'. Assume my character is a 10th-level monk (+20' speed), a 6th-level Barbarian (+10' speed from fast movement), a 2nd-level Rogue (with the cunning action feature), a 2nd-level Fighter (with the action surge feature), and has the mobile feat (+10' speed). This allows a speed of 70'. a partner casts longstrider on me (+10' speed), so my speed is 80'.
The tabaxi feline agility feature is: "when you move on your turn during combat, you can double your speed until the end of the turn, cannot be used again until you move 0".
Assuming I need to run - while in combat:
Base speed 80'
feline agility "when you move on your turn during combat, double speed" now speed 160'
action drink potion of speed (gain an additional action, doubles movement)
notice this does not double again, as an effect that already doubles my speed is in effect
haste action dash +160
action surge dash +160
bonus action dash (cunning action) +160
= 640 feet
Now the next turn, I couldn't use feline agility, nor action surge, but would free up an Action, and the haste spell effect would double my speed.
Recalculating this, base movement 80
potion of speed in effect x2 (160)
haste action dash +160 (320)
action dash +160 (480)
bonus action dash (cunning action) +160 (640)
As I understand it, if an effect would be repeated through use of item/magical means, they do not stack. In this case the "Doubles your movement" is the effect in question, as it is repeated through many means (spell, potions, racial abilities, and even boots) it only makes sense that it is not permitted to stack, but please, correct me if I am wrong.