Blade outer air seal with seal plate and flexible seal

A gas turbine engine comprising:

• a row of blade outer air seal arc segments arranged around an engine axis, each of the blade outer air seal arc segments including a ceramic matrix composite (CMC) body defining a core gaspath side, a non-core gaspath side opposite the core gaspath side, a forward end, an aft end, and circumferential sides, the CMC body having forward and aft flanges projecting from the non-core gaspath side;
• an annular seal plate located forward of the forward flange, the annular seal plate including a radially-extending wall, an axially-extending wall projecting forwardly from the radially-extending wall, and a nose projecting aftly from the radially-extending wall, the nose sealing against the forward flange;
• and
• a flexible seal located in a recess defined by the radially-extending wall and the axially-extending wall, the flexible seal sealing against a forward face of the radially-extending wall and the flexible seal being radially spaced apart from a radially outer face of the axially-extending wall.