Is 1....e6 a good and flexible move against 1.d4?

It would seem to me that the transformation to French by 2.d4 is at White's disposition rather than at Black's.

yes it is good and very flexible

1... Nf6 2... e6 is probably better, stopping a direct e4 plan. Unless you want to go into the French off course (:

1...e6 is  a  very coward move.  French deffense acording with Stenitz it has been the m0st b0ring opening ever in chess history 

It is the favourite opening f0r the bookkeepers

The big advantage is that move 2 jokes like Bg5 don't work against it, since the B drops. If you are going to play QGD or Nimzo it's an easy transposer. If you want to play other things like KID, not so much.

I used to use it as a Dutch transposer, but just switched it to QGD.

1..e6 is fine, but only if you are happy to play the French. I am not happy to play the French, otherwise I might sometimes play 1.e4, but that is very much my problem.

As a first move 1...e6 is very flexible, it can lead to a nimzo, dutch, benoni, QGD and the french. I play the french and the benoni, so 1...e6 will be my first move most of the time.

1.d4 e6 2.c4 Bb4+ is a unique path made possible by 1...e6 (referred to by Keene as the "Kangaroo" I believe.)  It may transpose to a Bogo but with Black's f-pawn unblocked there are occasionally chances to sneak an ..f5 in.

Also 1.d4 e6 2.Nf3 c5 is a good way to limit some of White's available systems provided you are okay with a Sicilian after 3.e4.

Absolutely.  Probably the best universal move you can play.

 Eingorn as a nice book , which covers the possibilites mentioned by GreenCastleBlock. There is also the English defence 2...b6, which is quite ambitious.

The problem with e6 against 1d4 IMHO is that if white carries on to play the London or Colle or g3 black can't really play g6 and Bg7 which I like against these insipid formations. Although white can still keep black guessing for another move with 2Nf3 if black plays 1...Nf6 which may be the most flexible first move of all for black against 1d4.

Deferring e6 also keep the option of developing the light squared bishop outside the pawn chain as well.

Any opening doesn't work for anyone at somepoint.  From the early 30's for about ten years, 1d4 e6 2c4 Bb4ch, was Keres main defence against 1.d4, including playing it twice at Avro 38'.  

The delay in playing Nf6 can also be used in other ways. For example, 3Nc3 c5 4d5 BxNch 5pxN then d6,e5 with a Nimzo style blockading position, were black can play ne7-g6.

If you can play a French, QGD, Nimzo and/or Queen's Indian Defense well, then it's ok.  I used to play e6, to suck d4 players into a French, which I knew very well at the time.  However, nowadays, I'd prefer not to block in my light squared bishop, just to keep white in suspense.   Instead of letting white choose between 2. e4 or c4, I'd now go with Nf3 and transpose into a QGD, Slav or Semi-slav.  I only play the French against 1. e4 these days (by transposition, after c5, Nc6, e6 and d5).   

1. d4 e6  2. c4 Bb4ch is actually called the Keres Defense now.  lol

Nobody has mentioned the possible transposition to a Sicilian, with 1.d4 e6 2. e4 c5 3. Nf3

I think that's actually called the Franco-Sicilian, since the d4 pawn is out there before c4 is played.  That can also transpose into a French, a Sicilian: Alapin's Variation or a Benoni.   But you're right.  I don't think anyone has suggested that move order yet.   

That position is more likely reached by 1.d4 e6 2.Nf3 c5 3.e4 which was mentioned earlier.

After 1.d4 e6 2.e4 c5, 3.Nf3 would be an odd choice considering White has the superior 3.d5 available.  3.c3 is also a good alternative.