Add API tab to Flatten all CNAMEs section

Author: RebeccaTamachiro

src/content/docs/dns/cname-flattening/index.mdx

@@ -26,5 +26,5 @@ For more details on the steps involved in `CNAME` flattening, review the [CNAME
 
 ## Aspects to keep in mind
 
-* `CNAME` flattening happens by default in some cases, as explained in its [Setup page](/dns/cname-flattening/set-up-cname-flattening/)
+* `CNAME` flattening happens by default in some cases. Refer to [Setup](/dns/cname-flattening/set-up-cname-flattening/) for details.
 * <Render file="cname-flattening-callout" />

src/content/docs/dns/cname-flattening/set-up-cname-flattening.mdx

@@ -27,10 +27,18 @@ If the `CNAME` target is on the same zone as the `CNAME` record, Cloudflare proc
 
 For zones on paid plans, you can choose to flatten all `CNAME` records. This option is useful for <GlossaryTooltip term="proxy status">DNS-only (unproxied)</GlossaryTooltip> `CNAME` records. [Proxied records](/dns/manage-dns-records/reference/proxied-dns-records/#proxied-records) are flattened by default as they return Cloudflare anycast IPs.
 
+<Tabs syncKey="dashPlusAPI"> <TabItem label="Dashboard">
+
 1. Log in to the [Cloudflare dashboard](https://dash.cloudflare.com/login) and select your account and domain.
 2. Go to **DNS** > **Settings**.
 3. Turn on the option **CNAME flattening for all CNAME records**.
 
+</TabItem> <TabItem label="API">
+
+Make a `PATCH` request to the [Update DNS Settings](/api/operations/dns-settings-for-a-zone-update-dns-settings) endpoint and set `flatten_all_cnames` to `true` in the request body.
+
+</TabItem> </Tabs>
+
 :::caution
  <Render file="cname-flattening-callout" />
 :::
@@ -51,7 +59,7 @@ Paid zones also have the option of flattening specific `CNAME` records.
 For the following cases, **Flatten** will not be available:
 - The record is at the [zone apex](#for-your-zone-apex).
 - The record is already proxied, which means it will be flattened by default.
-- **CNAME flattening for all CNAME records** is turned on, which means you cannot override it per-record.
+- **CNAME flattening for all CNAME records** is turned on, which means you cannot override it per record.
 :::
 
 </TabItem> <TabItem label="API">