I want to replace kitchen tile squares with linoleum.

Get a pro....measuring a huge piece around immovable objects accurately is VERY difficult.

A skilled handyman should be able to handle it. Double check his measurements

Are you asking if it is possible to remove kitchen tiles yourself, and then install new linoleum, as a diy project?

What is the aprox sq footage of the area you want to change?

What material are the tiles made out of?

I would go with the pro, a lot of things can go wrong and only the most skilled handymen can handle it. Professionals deal with issues every day that average handymen never see.

I vote for the handyman with one caveat..... Look at his previous jobs. The devil is in the details. Does his previous work reflect attention to detail? Look at corners, edges and joints. This should look professional. Vinyl flooring is not hard. You can lay down paper to template the cuts