Yup, just use CSS via the Kleo theme settings, replacing #f00 for whatever colour code you want….
Default wordpress sidebar search:
#searchform .input-group { background-color: #f00; }
Kleo main menu search pop-up panel:
#nav-menu-item-search .show_search_pop { background-color: #f00; }
And the search box itself:
#nav-menu-item-search .form-control { background-color: #f00; }
bbPress forums search:
.bbp-search-form { background-color: #f00; }
BuddyPress groups search form:
#search-groups-form { background-color: #f00; }
BuddyPress members search form:
#search-members-form { background-color: #f00; }
If you have a browser such as Google Chrome, you can right click any part of a web page and choose “Inspect Element” to see the HTML behind it and get class or id of tags.