Launch a screen flow from Process builder

Process builder cannot be used to launch an interactive flow (one with user screens), from Salesforce documentation an autolaunched flow:

Doesn’t require user interaction. This flow type doesn’t support screens, local actions, steps, choices, or dynamic choices.

SF Help on Flow Types

So that would not be an option for your scenario.

Either the Quote screen needs to be replaced with an interactive flow to update it so that the user can be directed or another approach would be required to capture the user input, such as sending a chatter message or email with the linked opportunity record prompting the user about changing the status.

Here is a quick and dirty example of an implementation via an Action on the Quote Object:

When the checkbox is changed, you can use a PB to update the related Opportunity.

To create an action, navigate to the Object Manager, choose Buttons, Links and Actions, and create a new Action. Choose to update a record, and select the checkbox field in the Page Layout. In the 'Predefined Field Values' section, set your Quote status to 'Accepted'.

Repeat the steps for a 'Quote Denied' action.