If this is in Chrome (the message you quote matches what I see there) you have two options:
1. click the padlock at the left hand end of the address bar, and at the bottom of the menu select Site Settings. Here you can set Lincs to the Past to allow Flash - and as far as I know, this is a permanent setting.
2. click the jigsaw icon with a red X towards the right of the address bar, then Manage. Here it appears you can allow Flash for any site until you close the browser.
Since Flash is inherently rather insecure the first option is better as it doesn't automatically allow Flash on random sites that you might visit later.
In Firefox you have to explicitly allow Flash for each site the first time you visit it in a session (with the brick icon towards the left of the address bar), and it remembers that until you close the browser.
Flash will be unsupported from the end of this year, and browsers will probably simply not run it. There was a recent thread about this in relation to Lincs to the Past, and I believe it was said that they are working on a new version of the site that doesn't use Flash.
