ガキ means “a kid” or “brat” in a rough way.
は is the particle which indicates the topic of the sentence.
らしく following a noun means “just like” or “just like how one always does” which is used to express something that the speaker thinks it’s a typical characteristic of someone or something. So ガキらしく means “just like kids” or “just like how kids always do”.
The particle よ in the middle of a sentence is used to make the tone strong, rough and manly.
ニカーッ is an onomatopoeia which expresses a grin or wide smile. The と particle following an onomatopoeia works as an adverb and explains a condition or way of being that exists at a particular time. For instance, if you use the onomatopoeia コロコロ with the verb 転がる meaning “to roll” which makes コロコロと転がる it expresses that something light is rolling but if it’s ゴロゴロと転がる it expresses something heavy is rolling. In this sentence, the verb modified with the adverb ニカーッと is 笑って which is the te-form of 笑う meaning “to smile” so ニカーッと笑う means “to smile widely“.
And a verb te-form followed by いこう means “should be doing something” used to express a suggestion or request in an encouraging and supportive way. So the verb usually has a positive meaning.
や is the sentence ending particle used by men when persuading equals or inferiors to do something in a rough and vulgar manner. It’s usually used with a verb volitional or imperative form.