Translation:I will give flowers to Mr. Tanaka.
Fellas, most of the time when it's a single Japanese name Duo is using the family name, just like they do in their culture (mostly). Tendency is family name first, individual second. If a single name is used you have to either know what kind of name it is or pay close attention to the context (level of formality / closeness between parties). A complete honorific drop is a severe case of disrespect among acquaintances or casualness between very close people.
In previous lessons we got that Tanaka and Honda are family names. Shigeru and Sakura are personal names. We had lessons coupling personal and family names before. Just relax and let the words soup duo provides sink in and your brain will connect the dots when you are relaxed eventually. For any specifics there's always the comments.
Most important: have fun!
But when translating to English you don't use -san. It's not English, it's Japanese in rōmaji. Adding -san to an English translation is foolish, I'd even go so far as to call it lazy. There's also no context available here to discern whether poor Tanaka here is an equal or a superior. As an equivalent example, you wouldn't call your classmate/friend/junior 'Ms. (Kate) Anderson.' Unless you're being weird and overly, almost creepily formal, you'd just call her Kate, right? So in the absence of such context, both 'Tanaka' or 'Ms/Mr Tanaka' should be accepted as correct for this answer.
In this lesson, the sentence 姉にスカートをもらいます is "My older sister gives me a skirt", and this sentence 田中さんに花をあげます is "I give flowers to Mr./Ms. Tanaka" - so would I be correct in saying the particle に here is indicating the person to whom the verb is referring? Just want to make sure I understand this usage of the particle correctly.
I know it has been a long term practice for educators to be giving an English interpretations of Japanese verbs in their present tense form by using the word "will". However "will" is actually refers to future time and often in future tense. So, if possible I would try to drop the modal verb "will" and just use a verb which in present tense form. And I know that makes the sentence in English sound a bit more stilted, but in actually it is more of an accurate reflection on how the Japanese sounds, which is very stilted.
San being translated seems kinda weird, San is an honourific given to everyone, Kun is a male honourific, Chan is a Female honourific, and chan and kun are also interchangeably used with friends it just seems weird for San to be translated when it's just part of Japanese culture