It can be argued the reduction in popularity of flash games is due to the rise and prominence of mobile games. There is certainly a correlation between the two because of the ubiquity of smartphones and their ability to play games which essentially are browser-based games. For the basis of my reply, I will argue that not only flash games but the entire browser-based gaming scene has declined.
The rise of mobile gaming has created a substitute to browser-based gaming. A substitute characterised by convenience and affordability. Mobile gaming has allowed people to play pseudo browser-based games wherever they want and when they want. This is an obvious constraint for the browser-based gamer, where their PCs are stationary and located at home, or their laptops are used for more important purposes than to play browser-based games. Therefore, mobile gaming has decreased the popularity of browser-based gaming.
However, the blame cannot be placed solely on mobile gaming, there are other culprits, such as the transfer of browser-based games to a mobile format. Although a consequence of the rise in mobile gaming, this should be isolated as its own factor. At the dawn of mobile gaming, most mobile games were new projects. Some were inspired by other games, some were completely revolutionary. But they were different from the established browser-based games/series, games and series that had devoted community followings. Currently, however, developers are increasingly porting their browser-based games for mobile use. Therefore, segmenting the communities between platforms, in favour of mobile gaming due to its convenience and affordability. The porting of games has contributed significantly to the further decline of browser-based gaming, as developers are developing more for the mobile market, the larger market, the more profitable market.
The mobile market offers a nearly unified platform to which games are advertised and presented: Google Play or the IOS App store. A luxury that browser-based gaming does not have. Browser-based games are segmented between different websites: Armorgames, Miniclip, Kongregate, Addictinggames, etc. Often these sites have exclusive games, such as Agar.io on Miniclip.
A further reason for the decline of the browser-based game is the simultaneous rise of non-browser-based PC games. Steam, being the most popular PC gaming platform, has an array of free-to-play games that have the capacity to surpass anything developed on browsers. There is a socially constructed view that browser-based games are inferior in quality, and non-browser-based games superior. Therefore, there is a shift in the platforms of where people play on PC. In the past, a large portion of PC gaming was done through browser-based games. At present, most PC gaming is done on Steam. This further divide of the PC gaming arena, only deteriorates whatever playerbase the browser-based gaming community has. A consequence of the rise of non-browser-based gaming is the increase in computing power of modern computers. PC gamers are conscious about their computer specifications, and many obtain high-level CPUs and GPUs for high fidelity and performance gameplay. With such investment in high-powered machines, it would seem a waste to play only flash games, enforcing the browser-based inferiority social construction.
However, based on a google trends comparison, the term "games" is searched very frequently. What is displayed when searching for "games" is a list of many browser-based websites. Depending on how many people use these browser-based game websites, it may appear that browser-based gaming may live for a longer period of time. But the term "games" is becoming increasingly less searched, in fact, it is currently at its lowest frequency in its entire google trend history. This may represent a decline in the browser-based gaming population.
Therefore, because of the rise of mobile gaming, porting games and non-browser-based PC games, it can be argued that browser-based gaming, and subsequently flash games, is declining at a rapid rate. The decreasing prevalence of "games" as a search term may further increase the decline, but at its present state, browser-based gaming will survive.