I help my kid cut his fingernails.
There is nothing wrong with the sentence; it makes sense. But, as it's in the present simple, it expresses the idea that you usually help your kid cut his fingernails when it's needed.
Let me help you cut your fingernails or let me cut your fingernails.
The first sentence is usually used when your kid is inclined to cut his fingernails at the time of speaking. On the other hand, the second sentence doesn't indicate whether he is inclined to this act at the time of speaking.
Moreover,when you help someone, the verb "help" can be followed by an infinitive with "to" or without "to".
So you can say "I help my kid ((to) cut his fingernails". "To"is optional.