Minecraft – How to add a “pet” particle to minecraft

You could use a setblock command, using a redstone block, instead of teleporting the player right away. The block would be placed next to some redstone, which would trigger a command block to say "teleporting", and run to a line of repeaters to create delay, which is what I assume you want. At the end, have it trigger two command blocks: One to teleport the player, the other to remove the redstone block, to ensure that this would work more than once. Here's a simple schematic:

     C2
C1   ^
R>>>>+>>C3

Where R is where the redstone block would be placed, C1 is the command block that would have the command to tell the player, C2 is the command block that destroys the redstone block, C3 is the command block that actually teleports the player. >> being a right-facing repeater, ^ being an up-facing repeater and + being redstone dust. You could also take advantage of the Scoreboard system so the command block teleports the correct player.

You probably want to loop the command slower. You can do this using redstone (just a regular redstone clock).

If you don't want to use redstone, you can tell the command block to only execute the command every few iterations.
To do this, you assign a timer scoreboard to the player that ticks up every game tick and only if it reaches the time you want, the sound gets played and then the timer gets reset.

Setup:

scoreboard objectives add timer dummy

In loop, replace @p with the selector of the flying player and ... with the rest of your playsound command:

scoreboard players add @p timer 1
playsound @p[scores={timer=20}] <...>
scoreboard players set @p[scores={timer=20}] timer 0

If it's a function, you can also use /schedule (archive):

/schedule function <function> 20

or:

/schedule function <function> 1s