here are the data types that correspond to the TYPE number returned by fetch_field. 

thought i would post this here since i couldn't find the info elsewhere.

numerics 
-------------
BIT: 16
TINYINT: 1
BOOL: 1
SMALLINT: 2
MEDIUMINT: 9
INTEGER: 3
BIGINT: 8
SERIAL: 8
FLOAT: 4
DOUBLE: 5
DECIMAL: 246
NUMERIC: 246
FIXED: 246

dates
------------
DATE: 10
DATETIME: 12
TIMESTAMP: 7
TIME: 11
YEAR: 13

strings & binary
------------
CHAR: 254
VARCHAR: 253
ENUM: 254
SET: 254
BINARY: 254
VARBINARY: 253
TINYBLOB: 252
BLOB: 252
MEDIUMBLOB: 252
TINYTEXT: 252
TEXT: 252
MEDIUMTEXT: 252
LONGTEXT: 252

The constants for the TYPE number returned by fetch_field are enumerated here (MYSQLI_TYPE_*):
http://php.net/manual/en/mysqli.constants.php

The flags used by MySql are:                                                                                                                                            
       NOT_NULL_FLAG = 1                                                                              
       PRI_KEY_FLAG = 2                                                                               
       UNIQUE_KEY_FLAG = 4                                                                            
       BLOB_FLAG = 16                                                                                 
       UNSIGNED_FLAG = 32                                                                             
       ZEROFILL_FLAG = 64                                                                             
       BINARY_FLAG = 128                                                                              
       ENUM_FLAG = 256                                                                                
       AUTO_INCREMENT_FLAG = 512                                                                      
       TIMESTAMP_FLAG = 1024                                                                          
       SET_FLAG = 2048                                                                                
       NUM_FLAG = 32768                                                                               
       PART_KEY_FLAG = 16384                                                                          
       GROUP_FLAG = 32768                                                                             
       UNIQUE_FLAG = 65536                                                                            

To test if a flag is set you can use & like so:
<?php
$meta = $mysqli_result_object->fetch_field();
if ($meta->flags & 4) { 
  echo 'Unique key flag is set'; 
} 
?>

Here are two methods for converting the 'type' and 'flags' attributes to text for debugging purposes. They both use the predefined MYSQLI_ constants to generate the text.

<?php

public static function h_type2txt($type_id)
{
    static $types;

    if (!isset($types))
    {
        $types = array();
        $constants = get_defined_constants(true);
        foreach ($constants['mysqli'] as $c => $n) if (preg_match('/^MYSQLI_TYPE_(.*)/', $c, $m)) $types[$n] = $m[1];
    }

    return array_key_exists($type_id, $types)? $types[$type_id] : NULL;
}

public static function h_flags2txt($flags_num)
{
    static $flags;

    if (!isset($flags))
    {
        $flags = array();
        $constants = get_defined_constants(true);
        foreach ($constants['mysqli'] as $c => $n) if (preg_match('/MYSQLI_(.*)_FLAG$/', $c, $m)) if (!array_key_exists($n, $flags)) $flags[$n] = $m[1];
    }

    $result = array();
    foreach ($flags as $n => $t) if ($flags_num & $n) $result[] = $t;
    return implode(' ', $result);
}

?>

The constants in a few other comments above appear to be inaccurate. Here are some more official references that seem quite hard to search.

The "type" attribute: https://dev.mysql.com/doc/internals/en/com-query-response.html#column-type
The "flags" attribute: https://github.com/google/mysql/blob/master/include/mysql_com.h#L133

In addition, all attributes are explained on the COM_QUERY_RESPONSE page too: https://dev.mysql.com/doc/internals/en/com-query-response.html#column-definition

The predefined constant values returned by the function get_predefined_constants() for:

MYSQLI_TYPE_CHAR = 1
MYSQLI _TYPE_TINYINT = 1

If the code is used to categorized the type of field use this values will of course create confusion. For example:

if($fieldtype === "CHAR"){
    $field_html_attribute = "text";
    $field_html_length = 1;
} elseif($fieldtype === "TINYINT") {
    $field_html_attribute = "number";
    $field_html_length = 1;
}

If an array is created to set the key as the numeric value and the value of that key as the the text title, TINYINT will be replaced by CHAR value. But is this process is reversed, then the code will select TINYINT if the foreach statement set to break when the numeric value of the flag equals the value of the current key as the first intance.

Base in the note added by Johnathan at http://php.net/manual/en/mysqli.field-count.php the values should be:

CHAR = 254
TINYINT = 1

But predefined function attributes the value 254 to MYSQLI_TYPE_STRING.

Just for FYI

It is not possible to get the values for an enum or set field through fetch_fields(). As far as I can tell this is because it hasn't been implemented in the mysqlnd api but whatever the reason it is not possible and you must issue a query like SHOW COLUMNS directly and interrogate the result to determine them.

Incidentally you need to check the enum_flag rather than look for the enum_type to determine whether a field is enum or not. The type returned is usually some kind of string.

Beware the values of the predefined constants.  They do not always correlate with the actual field types.  For example:

MYSQLI_TYPE_BLOB: 252
MYSQLI_TYPE_TINY_BLOB: 249
MYSQLI_TYPE_MEDIUM_BLOB: 250
MYSQLI_TYPE_LONG_BLOB: 251

MySQLi will indeed return a value of 252 for a tinytext field, but as you can see, this does not correspond to the value of MYSQLI_TYPE_TINY_BLOB.