2 note from comments, as this is accepted anyway.
source | link

It depends on the design. Some can't be washed properly, and milky liquids are much harder to clean off by rinsing than water or most water-based drinks

My genuine Thermos brand flask wouldn't be a problem because all the surfaces that come into contact with the food are accessible.

My previous small cheap flask had a pouring system in the lid that meant the contents passed through a non-washable chamber (clipped together in a way that wasn't designed to be opened). I eventually forced it open to find it full of hot chocolate residue. My flask is mainly used for kayaking, it has to be made up beforehand as fiddling about with powders when on a riverbank in the pouring rain doesn't tend to get you a hot drink when you need it. At that point it would have gone in the bin even if I hadn't just broken it.

A point mentioned in the comments is that the instructions for one particular Thermos say This product must NOT be used for keeping milk products or baby food warm or cool, to avoid the possibility of bacterial growth. This is the only reference to warm contents in these instructions; the word used elsewhere is hot (excluding washing-up instructions). Warm implies attempting to maintain temperatures in the danger zone. (for completeness as comments don't always last)

It depends on the design. Some can't be washed properly, and milky liquids are much harder to clean off by rinsing than water or most water-based drinks

My genuine Thermos brand flask wouldn't be a problem because all the surfaces that come into contact with the food are accessible.

My previous small cheap flask had a pouring system in the lid that meant the contents passed through a non-washable chamber (clipped together in a way that wasn't designed to be opened). I eventually forced it open to find it full of hot chocolate residue. My flask is mainly used for kayaking, it has to be made up beforehand as fiddling about with powders when on a riverbank in the pouring rain doesn't tend to get you a hot drink when you need it. At that point it would have gone in the bin even if I hadn't just broken it.

It depends on the design. Some can't be washed properly, and milky liquids are much harder to clean off by rinsing than water or most water-based drinks

My genuine Thermos brand flask wouldn't be a problem because all the surfaces that come into contact with the food are accessible.

My previous small cheap flask had a pouring system in the lid that meant the contents passed through a non-washable chamber (clipped together in a way that wasn't designed to be opened). I eventually forced it open to find it full of hot chocolate residue. My flask is mainly used for kayaking, it has to be made up beforehand as fiddling about with powders when on a riverbank in the pouring rain doesn't tend to get you a hot drink when you need it. At that point it would have gone in the bin even if I hadn't just broken it.

A point mentioned in the comments is that the instructions for one particular Thermos say This product must NOT be used for keeping milk products or baby food warm or cool, to avoid the possibility of bacterial growth. This is the only reference to warm contents in these instructions; the word used elsewhere is hot (excluding washing-up instructions). Warm implies attempting to maintain temperatures in the danger zone. (for completeness as comments don't always last)

1
source | link

It depends on the design. Some can't be washed properly, and milky liquids are much harder to clean off by rinsing than water or most water-based drinks

My genuine Thermos brand flask wouldn't be a problem because all the surfaces that come into contact with the food are accessible.

My previous small cheap flask had a pouring system in the lid that meant the contents passed through a non-washable chamber (clipped together in a way that wasn't designed to be opened). I eventually forced it open to find it full of hot chocolate residue. My flask is mainly used for kayaking, it has to be made up beforehand as fiddling about with powders when on a riverbank in the pouring rain doesn't tend to get you a hot drink when you need it. At that point it would have gone in the bin even if I hadn't just broken it.