Baby cry detection model using binary classification through logistic regression
As your context, You convert your audio clips to spectrogram images. The spectrogram is a visual representation of the spectrum of frequencies of sound.
 Now you need to Extract Features from your dataset. There are many feature extraction technique for audio data (See this blog for knowledge).
  The state of the art features extraction is now using:  MFCC — Mel-Frequency Cepstral Coefficients.
 By using librosa library we can easily implement the MFCC.
 Here are some resources for MFCC :

Music Feature Extraction in Python - From towardsdatascience
Audio Data Analysis Using librosa - Kaggle Notebook (Check out Mel-Frequency Cepstral Coefficients(MFCCs) portion)
Stack Overflow Question : MP3 to MFCC

After you extract features (Converted into MFCC), Then you need fit them into the Logistic Regression Model as you wanted. I share some resources which experiment with MFCC Features and Logistic Regression:

Classification Logistic Regression/SVM on mfccs
Audio-Genre-Classification GitHub repo by dhruvesh13 
Pitch detection - Kaggle Notebook

And for learn logistic regression, you may follow Machine Learning By Stanford, Coursera or follow this from youtube.