Hello and thank you for your question.
Yes, the partners that are selling a portion of their partnership interest will realize a gain(loss) equal to the difference between the amount realized and their basis in the interest sold. §741. The gain is generally capital in nature unless a portion of the interest is attributable to things like inventory and accounts receivable. §751.
If the partner earns the $6,250 by working in the partnership in the form of a guaranteed payment, then that amount is generally taxed to the partner earning the amount who can then pay off what is essentially a loan payable to the other partners for a sale of the 5% capital interest in the partnership. The guaranteed payment is deductible to the partnership in general, so would tend to more than offset the gain recognized by the partners selling their interests (ie., it would tend to be a deduction against ordinary income for the guaranteed payment while the partners tend to recognize only a capital gain on the sale of their shares).
The new member purchases from the two existing members a 2.5% capital and profits interest and owes them $3,125 each. The new member works for the LLC and receives a $6,250 guaranteed payment that is taxable to the new member and deductible by the partnership. The income assigned to the two existing members from the partnership is reduced by the guaranteed payment allocable to them. The existing members recognize a gain(loss) on the sale of their interests equal to the difference between the $3,125 received and their basis in the 2.5% interests they sold.
2.5% of each existing member's capital account is transferred to the new member.
Note that the capital account allocable to a member and that member's basis in a partnership interest are generally two very different things. The capital account can be negative and is generally the difference between the assets and liabilities of the partnership allocable to a member's interest. The member's basis cannot be negative and is equal to what the member paid for their interest plus all the income allocable to and any capital contributions made by the member to the partnership less any losses and distributions allocable to the member.
The gain that the existing members recognize on the sale of the partnership interest has nothing to do with their capital accounts, generally speaking. It is the difference between each member's amount realized and that member's basis in the interest sold. A member's basis is a very dynamic number as clarified above, does not appear anywhere on the partnership return, and is to be tracked by the member. It is not the partnership's responsibility to track any member's basis in their interest, but if the information is made available, good partnership return preparers will generally issue basis statements to the partners along with their Schedule K-1s.