Flatten an array

a = {{{w -> 0.25}}, {{w -> 0.05}}, {{w -> 0.190065}, {w -> 
    0.0182686}}, {{w -> 0.0404842}, {w -> 0.0086731}}, {{w -> 
    0.156634}, {w -> 0.015429}, {w -> 0.00478921}}, {{w -> 
    0.0344873}, {w -> 0.00753932}, {w -> 0.00292085}}, {{w -> 
    0.134788}, {w -> 0.0134812}, {w -> 0.00424987}, {w -> 
    0.00191167}}, {{w -> 0.0302949}, {w -> 0.00671401}, {w -> 
    0.0026321}, {w -> 0.00131905}}, {{w -> 0.119177}, {w -> 
    0.012046}, {w -> 0.00383985}, {w -> 0.0017433}, {w -> 
    0.000948279}}}

w /. a // Flatten

Flatten[lst][[All, -1]]

{0.25, 0.05, 0.190065, 0.0182686, 0.0404842, 0.0086731, 0.156634, 0.015429, 0.00478921, 0.0344873, 0.00753932, 0.00292085, 0.134788, 0.0134812, 0.00424987, 0.00191167, 0.0302949, 0.00671401, 0.0026321, 0.00131905, 0.119177, 0.012046, 0.00383985, 0.0017433, 0.000948279}

Also

Values @ Flatten @ lst

same result

Flatten @ Values @ lst

same result

Cases[lst, _Real, All]

same result

For the general case where you only want rules with the left-hand-side 'w':

Cases[{{{w->0.25}},{{w->0.05}},{{w->0.190065},{w->0.0182686}},{{w->0.0404842},{w->0.0086731}},{{w->0.156634},{w->0.015429},{w->0.00478921}},{{w->0.0344873},{w->0.00753932},{w->0.00292085}},{{w->0.134788},{w->0.0134812},{w->0.00424987},{w->0.00191167}},{{w->0.0302949},{w->0.00671401},{w->0.0026321},{w->0.00131905}},{{w->0.119177},{w->0.012046},{w->0.00383985},{w->0.0017433},{w->0.000948279}}},
 (w->x_):>x,
 \[Infinity]
]