You can directly name messages as LOG on line 4.

Be sure to terminate a statement with semi-colons.

Typically, you'd see reduce used to add up some values.

const totalLikes = entries.reduce((totalLikes, entry) => (totalLikes + entry.liked);

Nice job using the provided Timestamp component here.

Convention is to not have spaces around = sign when passing props

Spaces around curly braces when destructuring

Prefer not to have comments in code unless absolutely necessary.

Linter calls out that you're missing semi-colons. if you haven't configured your linter, you might want to do that so it can highlight syntax/style issues.

Would prefer to have this logic put in a method and the method get called somewhere.

Then on line 18, you can call the function:

    <div className={`chat-entry ${setLocalOrRemote()}`}>

It's more typical to see the result of using map referenced by a variable and using that variable in the JSX, like:

    const chatLogs =  entries.map((entry) => {
	      return (
	          <ChatEntry                                 
	            key={entry.id}
	            id={entry.id}
	            sender={entry.sender}
	            body={entry.body}
	            timeStamp={entry.timeStamp}
	            liked={entry.liked}
	            handleLike={handleLike}
	            currentUser={currentUser}
	          />
	        );
	     });
    };

  return (
        <div className="chat-log">
            {chatLogs}
        </div>
  );

Linter says "Block must not be padded by blank lines". Remove line 6

My linter shows all the style issues here. See the pink and green squiggley lines. I recommend configuring your linter so you can catch these issues before opening a PR.