In Flutter, how do I eliminate or minimize the vertical distance between two rows?

You can wrap Row With Container Widget and set the size According:

Example:

import 'package:flutter/cupertino.dart';
import 'package:flutter/material.dart';

class AudioPlayerScreen extends StatelessWidget {
  final String audioUrl;

  AudioPlayerScreen({required this.audioUrl});

  final double _audioIconSizeSmaller = 50;

  final double _audioIconSizeMedium = 60;

  final double _audioIconSizeLarge = 90;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('Audio Player'),
      ),
      body: Column(
        mainAxisAlignment: MainAxisAlignment.center,
        crossAxisAlignment: CrossAxisAlignment.stretch,
        children: [
          _buildPositionButtons(),
        ],
      ),
    );
  }

  Widget _buildPositionButtons() {
    return IntrinsicHeight(
      child: Column(
        mainAxisAlignment: MainAxisAlignment.center,
        children: [
          Row(
            mainAxisAlignment: MainAxisAlignment.spaceBetween,
            children: [
              Expanded(
                child: IconButton(
                  iconSize: _audioIconSizeMedium,
                  onPressed: () => print(''),
                  icon: const Icon(Icons.fast_rewind),
                ),
              ),
              Expanded(
                child: IconButton(
                  iconSize: _audioIconSizeSmaller,
                  onPressed: () => print(''),
                  icon: const Icon(Icons.fast_rewind),
                ),
              ),
              Expanded(
                child: IconButton(
                  iconSize: _audioIconSizeSmaller,
                  onPressed: () => print(''),
                  icon: const Icon(Icons.fast_forward),
                ),
              ),
              Expanded(
                child: IconButton(
                  iconSize: _audioIconSizeMedium,
                  onPressed: () => print(''),
                  icon: const Icon(Icons.fast_forward),
                ),
              ),
            ],
          ),
          Container(
            height: 10.0,
            child: Row(
              mainAxisAlignment: MainAxisAlignment.spaceBetween,
              children: const [
                Expanded(
                  child: Text(
                    '1 m',
                    textAlign: TextAlign.center,
                    style: TextStyle(fontSize: 20.0),
                  ),
                ),
                Expanded(
                  child: Text(
                    '10 s',
                    textAlign: TextAlign.center,
                    style: TextStyle(fontSize: 18.0),
                  ),
                ),
                Expanded(
                  child: Text(
                    '10 s',
                    textAlign: TextAlign.center,
                    style: TextStyle(fontSize: 18.0),
                  ),
                ),
                Expanded(
                  child: Text(
                    '1 m',
                    textAlign: TextAlign.center,
                    style: TextStyle(fontSize: 20.0),
                  ),
                ),
              ],
            ),
          ),

        ],
      ),
    );
  }
}