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Time is measured in turns not seconds

In D&D 5e, movement and actions do not consume time, they consume actions. The game is inherently turn based. Actions happen in sequence, with each happening completely before the next can begin. The one exception is Readied Actions, which may interrupt other actions during a turn.

In the case of Readied Actions, once the trigger occurs the action happens as soon as the triggering action is completed. Then the readied action takes place, completely, before resuming normal initiative order.

To understand this lets look at the rules for the Ready Action:

(...) you can take the Ready action on your turn, which lets you act using your reaction before the start of your next turn. (...)

When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. (...) If the reaction interrupts another creature's turn, that creature can continue its turn right after the reaction. (Chapter 9: Actions in Combat, PHB)

The Ready Action lets you perform an act in response to a trigger using your Reaction. This act can be anything you could have done on your turn with your Action, in this case the Owl is readying the Dash action.

To determine when this happens we need to look at what it means to use your Reaction. A reaction is defined as (emphasis mine):

A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else's. (Chapter 9: The Order of Combat, PHB)

When you trigger then Owl's movement, it instantly responds by moving to the desired position. Then you "continue [your] turn right after the reaction".

Case 1

The sequence of events for initiative order Owl -> Kobold -> Target is as follows (note; I have left out bonus actions, which can be taken at any point in the turn):

1. On the Owl's turn:
   1. Owl uses its movement to fly up to the target.
   2. Owl uses its action to Ready movement to move to a set position when Kobold signals it.
   3. Owl's turn ends.
2. On the Kobold's turn:
   1. Kobold uses its action to Attack. Getting as many attacks as it can take with the Attack action.
   2. Kobold uses a free activity on their turn to signal the Owl.
   3. Owl's readied action triggers. Owl moves to position.
   4. Kobold's turn ends.
3. Target's turn

Case 2

The sequence of events for initiative order Owl -> Target -> Kobold is as follows:

1. On the Owl's turn:
   1. Owl uses its movement to fly to a safe place.
   2. Owl uses its action to Ready movement to move next to the target when Kobold signals it.
   3. Owl's turn ends.
2. Target's turn
3. On the Kobold's turn:
   1. Kobold uses a free activity on their turn to signal the Owl.
   2. Owl's readied action triggers. Owl moves to position.
   3. Kobold uses its action to Attack. Getting as many attacks as it can take with the Attack action.
   4. Kobold's turn ends.

In both cases the Kobold can get its full turn of actions/attacks with benefit of Pack Tactics. This is the combat system working as intended.

A Caveat

It is worth pointing out that this will be more difficult to pull off with more than one target as the initiative order won't always suit you. Also targets could Ready an Action to attack the Owl when it comes within range, which would trigger before the Kobold's attacks, potentially negating Pack Tactics.

D&D isn't a realistic combat system

The combat system in D&D does not attempt to replicate a realistic combat environment. Ideas such as movement taking time or actions occurring simultaneously are not compatible with the game.

The game organizes the chaos of combat into a cycle of rounds and turns. A round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn. (Chapter 9: The Order of Combat, PHB)

While your attempts to make this logical and account for realistic movement are admirable, they do not align with the actual rules of combat and action resolution. Rounds, Turns and Actions are an abstraction of game-time passing. A round is approximately 6 seconds but turns do not resolve in real-time. Their resolve mechanically in initiative order, which follows the sequence I have laid out above.

Were I to DM this situation, I would allow it exactly as the rules intend. You, however, are free to house-rule any modification you wish. Simply discuss it with your DM as it is their ruling that will matter at the table.