「肉入{にくいり}」 (also written as 「肉入{にくい}り」) simply means "(an amount of) meat contained".
The phrase is used forto describe dishes that contain small amounts of meat. It is not used with obvious meat dishes such as steaks, beef stew, etc.
You will keep encountering the phrase:
「[Food item] + 入り入{い}り」
at eateries and grocery stores.
FYI: In case you want to order the dish prepared without that particular food item, the phrase to use is explained in this Q&A.