If your kitten's purr sounds heavy and like it has phlegm, it could be a sign of a cold. Additionally, a monotonous diet lacking in essential nutrients or cold weather can also cause a kitten’s purr to sound abnormal.

Three Reasons Why a Kitten's Purr Might Sound Like It Has Phlegm
1. Common Cold
A heavy, phlegm-like purr is often a symptom of a cold in kittens. Make sure to keep your kitten warm, and provide appropriate treatment. You can consider using kitten-specific cold remedies. Avoid giving your cat human cold medications, as cat colds are different, and improper dosing can lead to complications. If you're unsure, consult with a vet.
2. Nutritional Deficiency
Nutrient deficiencies can also lead to a heavy-sounding purr. Ensure your kitten receives a balanced diet. In addition to cat food and water, consider introducing supplementary foods like carrots, meat purees, fish broth, or chicken liver porridge. If preparing these meals isn't feasible, convenient options like nutritional pastes or cat food cans are readily available.
3. Cold Weather
When kittens feel cold, they may exhibit symptoms resembling a congested nose and phlegmy breathing. Prioritize keeping your kitten warm. Avoid exposing them to air conditioning or fans, and prevent them from sleeping on cold floors. Instead, consider providing a cooling mat or a sleeping pad for them to rest on. Ensuring your kitten has adequate warmth can help improve their breathing and purring.