Looking for an idea to make the bookcase look flush against the wall.

Hello Piw, My first thought was perhaps some base cap moulding applied flush against the wall and wood glued to the side of the cabinet (I don't know whether or not you rent). Then I thought I'd look online for a solution and the only things I found involved removing the baseboard, building a framework that is attached to the wall, then adding the bookcase to that, and replacing the baseboard around the bottom of the bookcase. Or perhaps if you just attached it to the wall (so it doesn't fall over somehow), that might work. I don't know how much work you want to do but I've included a link below. Good Luck to you with this project, and thanks for asking Hometalk for answers :)

https://www.todayshomeowner.com/video/how-to-secure-tall-furniture/

you could try getting the slim cut corner moulding and put it around the the bookshelf to make it look like it's built into the wall. just an idea hope it helps.

You could try raising it up to get it more flush. Attach a board on the bottom.

Add molding or trim.

we have three sided (long piece on front and short pieces on sides) to support the bookcases on the floor and raise them over the baseboards. they are set in under the bookcases so don't really show. They are also stained to match the floor and not the bookcases.

Shoe molding glued to the bookcase

Cut out more of the existing cutout on the bookcase to fit your baseboard.

I see! The cutout ends with the shelf. I would use pieces of 1"X2" board, paint them white and slip them under the each side to raise the bookcase so the cutout would fit your baseboard. It would be like shimming it up. Then you can push the bookcase against the wall. You can even use double stick tape to stick the "shims" to the bottom of the sides. This way they can be removed if ever needed.

No, it's even smaller. Sometimes called cabinet scribe.

How about some lengths of small quarter round with finishing nails?

Its rather cheap and will make the bookcase more finished looking...may look more built in.

Stain the quarter round the same color as the bookcase.

Instead of filling in the gap with wood, what about using wide upholstery piping, also sometimes called gimp trim? Tuck it into the gap and attach with staples. Picture below also shows the same concept using sisel rope.

Run a length of skirting around the bookcase to match existing. Stick on with double sised tape.

Quarter round cut to size and painted to match the bookcase.

Can you send a pic and description of how you resolved the issue, please?

Either cut out more of the backboard to allow it to be pushed back, or Put the bookcase on a plinth to lift it up so it will fit your skirting.