Is it possible to escape from a wall of stone spell on the turn it is cast by flying?

The spell wall of stone allows those that might be trapped by it a chance to escape during the action in which it is ‘springing into existence’.

If a creature would be surrounded on all sides by the wall (or the wall and another solid surface), that creature can make a Dexterity saving throw. On a success, it can use its reaction to move up to its speed so that it is no longer enclosed by the wall.

Consider a caster making a wall with a roof to enclose a creature with flying movement capability.

Suppose the horizontal distance from the creature to any point outside the wall is greater than its speed so that even a successful Dex save will not allow it to escape enclosure.

Further suppose that because the wall is wider and longer than it is high, the creature is capable of moving outside the wall vertically, if it is allowed to use its flying speed.

Does "its speed" in the spell description include flying speed?

It seems common sense that if a flying creature could walk out of the area enclosed by the wall as a reaction, it could also fly out of the area, but does RAW allow this? If I understand correctly, using "speed" does not subsume all forms of speed, but means walking speed only, sensu stricto.

"Speed" (PHB) (emphasis mine)

Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round.

"Speed" (MM 8) (emphasis mine)

SPEED A monster’s speed tells you how far it can move on its turn. For more information on speed, see the Player’s Handbook.
All creatures have a walking speed, simply called the monster’s speed. Creatures that have no form of ground-based locomotion have a walking speed of 0 feet.
Some creatures have one or more of the following additional movement modes
FLY
A monster that has a flying speed can use all or part of its movement to fly.

If the description of the wall of stone spell allows only a creature’s speed to be used in its reaction, does "speed" mean only its walking speed since it is not otherwise specified? Although the creature has a flying speed, this is an ‘additional movement mode’ that is not designated by the spell’s permitted use of speed?

Suppose that flying speed may be used to escape the wall. The trigger for permitting the creature’s reactive movement is it being "surrounded on all sides" [sic]. If not surrounded, then, it appears that no reaction is permitted. Thus, if flying movement is permitted, does making the wall of stone appear without a roof mean that the creature is not surrounded by the wall, and thus is not permitted its reaction to attempt to escape?

Of course, without a roof the creature could then fly out on its next turn, but a lot could happen between the caster’s turn and the creature’s turn. Interestingly, if flying movement was a permitted form of reaction, the caster could then make a much smaller wall to still enclose the creature. The horizontal distance to the walls could now be made within the distance the creature could walk, and it would still not be allowed a reaction, since leaving off the roof would mean that it was not surrounded.

Is it possible to escape a roofed wall of stone on the turn it is cast by flying?
If so, can this escape be prevented by casting the wall without a roof?