You can achieve that overall layout by placing the search widget in the header widget area and setting your navigation location to float right.
Then you can add this CSS:
.inside-header {
display: flex;
align-items: center;
}
.site-logo {
order: 1;
}
.header-widget {
order: 2;
margin-left: auto;
top: auto !important;
margin-right: 20px;
}
.main-navigation {
order: 3;
}
Depending on browser support needed, you may want to run it through this tool: https://autoprefixer.github.io/
Then it will likely need some CSS tweaking for style.