Change the subpage search text color to --paper-gray-800.

chrome/browser/resources/settings/settings_page/settings_subpage_search.html

 <link rel="import" href="chrome://resources/cr_elements/cr_search_field/cr_search_field_behavior.html">
 <link rel="import" href="chrome://resources/html/polymer.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/paper-input/paper-input-container.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/paper-input/paper-input.html">
 
 <dom-module id="settings-subpage-search">
   <template>
     <style>
       paper-input-container {
         width: var(--paper-input-max-width);
       }
 
       input[type='search']::-webkit-search-cancel-button {
         -webkit-appearance: none;
       }
 
       #prompt,
       #searchInput {
-        color: var(--google-grey-500);
         font-size: 13px;
         line-height: 36px;
       }
 
+      #prompt {
+        color: var(--google-grey-500);
+      }
+
+      #searchInput {
+        color: var(--paper-grey-800);
+      }
+
       #clearSearch {
         -webkit-margin-end: -8px;
         -webkit-margin-start: 8px;
       }
 
       :root {
         --paper-icon-button {
           height: 36px;
           width: 36px;
         }
 
         --paper-input-suffix: {
           /* Required to align the icon in |clearSearch| vertically. */
           line-height: 0;
         }
       }
     </style>
     <paper-input-container no-label-float on-search="onSearchTermSearch">
       <label id="prompt">[[label]]</label>
       <input is="iron-input" id="searchInput" type="search"
           aria-labelledby="prompt" incremental>
       </input>
       <paper-icon-button suffix icon="cr:cancel" id="clearSearch"
           on-tap="onTapClear_" title="[[clearLabel]]" hidden$="[[!lastValue_]]">
       </paper-icon-button>
     </paper-input-container>
   </template>
   <script src="settings_subpage_search.js"></script>
 </dom-module>