Can I play an OTB game with a friend using chess.com app? I mean two physical players using only one phone/tablet.

There is a Pass and Play feature in the apps that is designed to do that.

Which app are you using?

Android tablet. 

I found it!

I wish however there was a mode where board does not flip, but the pieces do. I mean so that the player who is to move get to see the pieces correct (not upside down).

I think there is an options  feature for that that can turn off the auto-flip.

Yeah but I would like the icons of the pieces to flip, otherwise one player will see them upside-down. 

But what about the IOS version of the app ? No support OTB ?

I am pretty sure that Pass and Play is available on the IOS app too.

How do I 'pass and play' on my mobile device? (iOS)

If you're with a friend in person and want to play chess together, but don't have a board, don't worry! As long as you have the Chess.com app on your mobile device, you can play right there on the digital board!

Tap 'New Game' in the bottom of your home screen. Then tap 'More' to see additional options. From there, select Pass and Play! 

In the next screen you'll be able to choose from a list of options before you start the game: 

Type- You can choose between Standard, Chess960, a custom starting position. or a 'Key position.' Key position will let you choose from a list of premade positions, such as Two-Bishop mate, King and pawn vs king, and so on. 

Show best moves- Enable if you want to be shown a selection of good moves

Show threats- Enable if you want to be shown when a piece is under attack

Warn on mistakes- Enable to be warned if you are about to play a blunder

Board Flips- This will flip the board after each move. If you disable this, you will have to flip the board manually each move by tapping 'options' and then 'flip board' 

When you're ready, tap 'Play' and enjoy a game of chess in person, over a digital board!

Does not work with my Millenium T55 board.

https://www.youtube.com/watch?v=EC6HyZtg4XQ

My friend has the android app and it works - but it do not work with IOS!

In the Video the tablet is Android too.

i late but they have pass and play on lichess app where it dosmt flip the board but the icons face its side