Yes, but you'll have to do it manually.
A dialogue cutscene can be done by creating a new hidden layer for the text box, which changes the contents of the text every time the player presses the confirm key, hiding and showing itself when prompted.
Set up an activation condition (i.e. player overlaps X,Y) and have the layer unhide itself. Make sure you disable the player-controlled movement behavior first. I know some people who enter the text into the event sheets and link them to a numbered variable which goes up each time the player presses the confirmation button, and some people reference the text from an INI or other text-based file.
There are a few ways to stop input and manipulate player and enemy movements, which is probably the most important part of a cutscene. Look through behavior actions for something that will help.
You can have things going on in the background, like rocks falling into the entrance or a bunch of chickens doing a little dance. Use behaviors and animations to allow objects to move. Think creatively; experiment with the engine and apply the results of said experimentation to your project.
I don't know about Flash support, but I'm pretty sure Construct accepts some movie formats that Macromedia Flash files could be exported as.
Sorry if I'm being a bit vague, but I'm a wee bit tired at the moment.