First try at adding a flatMap spec

spec.bs

@@ -827,9 +827,72 @@ For now, see [https://github.com/wicg/observable#operators](https://github.com/w
 <div algorithm>
   The <dfn for=Observable method><code>flatMap(|mapper|)</code></dfn> method steps are:
 
-    1. <span class=XXX>TODO: Spec this and use |mapper|.</span>
+    1. Let |sourceObservable| be [=this=].
+
+    1. Let |observable| be a [=new=] {{Observable}} whose [=Observable/subscribe callback=] is an algorithm that takes a {{Subscriber}} |subscriber| and does the following:
+
+       1. Let |queue| be a new [=list=] to keep track of items emitted by the source observable that need to be processed.
+
+       1. Let |activeInnerSubscription| be false, indicating whether an inner subscription is currently active.
+
+       1. Let |sourceObserver| be a new [=internal observer=], initialized as follows:
+
+          : [=internal observer/next steps=]
+          :: 1. If |activeInnerSubscription| is true, then:
+
+                1. [=list/Append=] the passed in <var ignore>value</var> to |queue|.
+
+                1. Return.
+
+             1. Otherwise:
+
+                1. Set |activeInnerSubscription| to true.
+
+                1. Let |innerObservable| be the result of [=Invoke=] |mapper| with the passed in <var ignore>value</var>.
+
+                    If <a spec=webidl lt="an exception was thrown">an exception |E| was thrown</a>,
+                    then run |subscriber|'s {{Subscriber/error()}} method, given |E|, and abort these
+                    steps.
+
+             1. Let |innerObserver| be a new [=internal observer=], initialized as follows:
+
+                : [=internal observer/next steps=]
+                :: Run |subscriber|'s {{Subscriber/next()}} method, given the passed in <var ignore>value</var>.
+
+                : [=internal observer/error steps=]
+                :: Run |subscriber|'s {{Subscriber/error()}} method, given the passed in <var ignore>error</var>.
+
+                : [=internal observer/complete steps=]
+                :: 1. If |queue| is not empty, then:
+
+                      1. Let |nextValue| be [=list/Remove=] the first item from |queue|.
+
+                      1. Repeat the steps above starting from the step where |innerObservable| is obtained by invoking |mapper| with |nextValue|.
+
+                   1. Otherwise:
+
+                      1. Set |activeInnerSubscription| to false.
+
+                      1. If |sourceObserver| has also completed, run |subscriber|'s {{Subscriber/complete()}} method.
+
+             1. Let |innerOptions| be a new {{SubscribeOptions}} whose {{SubscribeOptions/signal}} is |subscriber|'s [=Subscriber/signal=].
+
+             1. <a for=Observable lt="subscribe to an Observable">Subscribe</a> to |innerObservable| given |innerObserver| and |innerOptions|.
+
+          : [=internal observer/error steps=]
+          :: Run |subscriber|'s {{Subscriber/error()}} method, given the passed in <var ignore>error</var>.
+
+          : [=internal observer/complete steps=]
+          :: If |activeInnerSubscription| is false, and |queue| is empty, run |subscriber|'s {{Subscriber/complete()}} method.
+
+       1. Let |options| be a new {{SubscribeOptions}} whose {{SubscribeOptions/signal}} is |subscriber|'s [=Subscriber/signal=].
+
+       1. <a for=Observable lt="subscribe to an Observable">Subscribe</a> to |sourceObservable| given |sourceObserver| and |options|.
+
+    1. Return |observable|.
 </div>
 
+
 <div algorithm>
   The <dfn for=Observable method><code>finally(|callback|)</code></dfn> method steps are: