Code for a pushbutton to produce an enable signal for a time delay generator

There are a few changes I would recommend.

First - I highly suggest you do not use the button as a clock. It will be very bouncy and generate a lot of edges, as well as having timing issues. You need to synchronise the button press into the clock domain and then detect the edge (using an edge detector, not a rising edge VHDL statement).

Secondly, your process in the delay_jen entity is not a clocked process. Just including the clock in the sensitivity list does not make it a clocked process. You need to follow the template. I also suggest you forget about variables for now - they will only get you in to trouble. Use signals instead.

signal count    : integer;
process(clk)
    
begin
    if rising_edge(clk) then
        if (en) then 
            flag<='1'; 
            count <= count+1;
            
            if (count=delay) then 
                count:=0; 
                flag<='0'; 
            end if;
        end if;
     end if         
end process;